diff --git a/frame/1m/packm/bli_packm_init.c b/frame/1m/packm/bli_packm_init.c
index 404498d60..0437b722a 100644
--- a/frame/1m/packm/bli_packm_init.c
+++ b/frame/1m/packm/bli_packm_init.c
@@ -56,8 +56,8 @@ siz_t bli_packm_init
 	bool_t    does_invert_diag;
 	bool_t    rev_iter_if_upper;
 	bool_t    rev_iter_if_lower;
-	//pack_t    pack_schema;
-	packbuf_t pack_buf_type;
+	pack_t    schema;
+	//packbuf_t pack_buf_type;
 	siz_t     size_needed;
 
 	// Check parameters.
@@ -70,8 +70,8 @@ siz_t bli_packm_init
 	does_invert_diag  = bli_cntl_packm_params_does_invert_diag( cntl );
 	rev_iter_if_upper = bli_cntl_packm_params_rev_iter_if_upper( cntl );
 	rev_iter_if_lower = bli_cntl_packm_params_rev_iter_if_lower( cntl );
-	//pack_schema       = bli_cntl_packm_params_pack_schema( cntl );
-	pack_buf_type     = bli_cntl_packm_params_pack_buf_type( cntl );
+	schema            = bli_cntl_packm_params_pack_schema( cntl );
+	//pack_buf_type     = bli_cntl_packm_params_pack_buf_type( cntl );
 
 #if 0
 	// Let us now check to see if the object has already been packed. First
@@ -112,30 +112,51 @@ siz_t bli_packm_init
 		return 0;
 	}
 
-	// We now ignore the pack_schema field in the control tree and
-	// extract the schema from the context, depending on whether we are
-	// preparing to pack a block of A or panel of B. For A and B, we must
-	// obtain the schema from the context since the induced methods reuse
-	// the same control trees used by native execution, and those induced
-	// methods specify the schema used by the current execution phase
-	// within the context (whereas the control tree does not change).
+#if 0
 	pack_t schema;
 
-	if ( pack_buf_type == BLIS_BUFFER_FOR_A_BLOCK )
+	if ( bli_cntx_method( cntx ) != BLIS_NAT )
 	{
-		schema = bli_cntx_schema_a_block( cntx );
+		// We now ignore the pack_schema field in the control tree and
+		// extract the schema from the context, depending on whether we are
+		// preparing to pack a block of A or panel of B. For A and B, we must
+		// obtain the schema from the context since the induced methods reuse
+		// the same control trees used by native execution, and those induced
+		// methods specify the schema used by the current execution phase
+		// within the context (whereas the control tree does not change).
+
+		if ( pack_buf_type == BLIS_BUFFER_FOR_A_BLOCK )
+		{
+			schema = bli_cntx_schema_a_block( cntx );
+		}
+		else if ( pack_buf_type == BLIS_BUFFER_FOR_B_PANEL )
+		{
+			schema = bli_cntx_schema_b_panel( cntx );
+		}
+		else // if ( pack_buf_type == BLIS_BUFFER_FOR_C_PANEL )
+		{
+			schema = bli_cntl_packm_params_pack_schema( cntl );
+		}
 	}
-	else if ( pack_buf_type == BLIS_BUFFER_FOR_B_PANEL )
+	else // ( bli_cntx_method( cntx ) == BLIS_NAT )
 	{
-		schema = bli_cntx_schema_b_panel( cntx );
+		// For native execution, we obtain the schema from the control tree
+		// node. (Notice that it doesn't matter if the pack_buf_type is for
+		// A or B.)
+		schema = bli_cntl_packm_params_pack_schema( cntl );
 	}
-	else // if ( pack_buf_type == BLIS_BUFFER_FOR_C_PANEL )
+	// This is no longer needed now that we branch between native and
+	// non-native cases above.
+#if 0
+	if ( pack_buf_type == BLIS_BUFFER_FOR_C_PANEL )
 	{
 		// If we get a request to pack C for some reason, it is likely
 		// not part of an induced method, and so it would be safe (and
 		// necessary) to read the pack schema from the control tree.
 		schema = bli_cntl_packm_params_pack_schema( cntl );
 	}
+#endif
+#endif
 
 	// Prepare a few other variables based on properties of the control
 	// tree.
diff --git a/frame/3/bli_l3_cntl.c b/frame/3/bli_l3_cntl.c
index 0ea06715a..33c64edcb 100644
--- a/frame/3/bli_l3_cntl.c
+++ b/frame/3/bli_l3_cntl.c
@@ -45,6 +45,21 @@ void bli_l3_cntl_create_if
        cntl_t** cntl_use
      )
 {
+	// This is part of a hack to support mixed domain in bli_gemm_front().
+	// Sometimes we need to specify a non-standard schema for A and B, and
+	// we decided to transmit them via the schema field in the obj_t's
+	// rather than pass them in as function parameters. Once the values
+	// have been read, we immediately reset them back to their expected
+	// values for unpacked objects. Notice that we do this even if the
+	// caller passed in a custom control tree; that's because we still need
+	// to reset the pack schema of a and b, which were modified by the
+	// operation's _front() function.
+	pack_t schema_a = bli_obj_pack_schema( a );
+	pack_t schema_b = bli_obj_pack_schema( b );
+
+	bli_obj_set_pack_schema( BLIS_NOT_PACKED, a );
+	bli_obj_set_pack_schema( BLIS_NOT_PACKED, b );
+
 	// If the control tree pointer is NULL, we construct a default
 	// tree as a function of the operation family.
 	if ( cntl_orig == NULL )
@@ -53,7 +68,7 @@ void bli_l3_cntl_create_if
 		     family == BLIS_HERK ||
 		     family == BLIS_TRMM )
 		{
-			*cntl_use = bli_gemm_cntl_create( family );
+			*cntl_use = bli_gemm_cntl_create( family, schema_a, schema_b );
 		}
 		else // if ( family == BLIS_TRSM )
 		{
@@ -62,7 +77,7 @@ void bli_l3_cntl_create_if
 			if ( bli_obj_is_triangular( a ) ) side = BLIS_LEFT;
 			else                              side = BLIS_RIGHT;
 
-			*cntl_use = bli_trsm_cntl_create( side );
+			*cntl_use = bli_trsm_cntl_create( side, schema_a, schema_b );
 		}
 	}
 	else
diff --git a/frame/3/bli_l3_oapi.c b/frame/3/bli_l3_oapi.c
index 5f4bc9932..94e563c24 100644
--- a/frame/3/bli_l3_oapi.c
+++ b/frame/3/bli_l3_oapi.c
@@ -57,20 +57,25 @@ void PASTEMAC(opname,EX_SUF) \
 \
 	BLIS_OAPI_CNTX_DECL \
 \
-	/* Invoke the operation's "ind" function--its induced method front-end.
-	   This function will call native execution for real domain problems.
-	   For complex problems, it calls the highest priority induced method
-	   that is available (ie: implemented and enabled), and if none are
-	   enabled, it calls native execution. */ \
-	PASTEMAC(opname,ind) \
-	( \
-	  alpha, \
-	  a, \
-	  b, \
-	  beta, \
-	  c, \
-	  cntx  \
-	); \
+	/* Only proceed with an induced method if all operands have the same
+	   (complex) datatype. If any datatypes differ, skip the induced method
+	   chooser function and proceed directly with native execution, which is
+	   where mixed datatype support will be implemented (if at all). */ \
+	if ( bli_obj_dt( a ) == bli_obj_dt( c ) && \
+	     bli_obj_dt( b ) == bli_obj_dt( c ) && \
+	     bli_obj_is_complex( c ) ) \
+	{ \
+		/* Invoke the operation's "ind" function--its induced method front-end.
+		   For complex problems, it calls the highest priority induced method
+		   that is available (ie: implemented and enabled), and if none are
+		   enabled, it calls native execution. (For real problems, it calls
+		   the operation's native execution interface.) */ \
+		PASTEMAC(opname,ind)( alpha, a, b, beta, c, cntx ); \
+	} \
+	else \
+	{ \
+		PASTEMAC(opname,nat)( alpha, a, b, beta, c, cntx ); \
+	} \
 }
 
 GENFRONT( gemm )
@@ -96,16 +101,25 @@ void PASTEMAC(opname,EX_SUF) \
 \
 	BLIS_OAPI_CNTX_DECL \
 \
-	PASTEMAC(opname,ind) \
-	( \
-	  side, \
-	  alpha, \
-	  a, \
-	  b, \
-	  beta, \
-	  c, \
-	  cntx  \
-	); \
+	/* Only proceed with an induced method if all operands have the same
+	   (complex) datatype. If any datatypes differ, skip the induced method
+	   chooser function and proceed directly with native execution, which is
+	   where mixed datatype support will be implemented (if at all). */ \
+	if ( bli_obj_dt( a ) == bli_obj_dt( c ) && \
+	     bli_obj_dt( b ) == bli_obj_dt( c ) && \
+	     bli_obj_is_complex( c ) ) \
+	{ \
+		/* Invoke the operation's "ind" function--its induced method front-end.
+		   For complex problems, it calls the highest priority induced method
+		   that is available (ie: implemented and enabled), and if none are
+		   enabled, it calls native execution. (For real problems, it calls
+		   the operation's native execution interface.) */ \
+		PASTEMAC(opname,ind)( side, alpha, a, b, beta, c, cntx ); \
+	} \
+	else \
+	{ \
+		PASTEMAC(opname,nat)( side, alpha, a, b, beta, c, cntx ); \
+	} \
 }
 
 GENFRONT( hemm )
@@ -129,14 +143,24 @@ void PASTEMAC(opname,EX_SUF) \
 \
 	BLIS_OAPI_CNTX_DECL \
 \
-	PASTEMAC(opname,ind) \
-	( \
-	  alpha, \
-	  a, \
-	  beta, \
-	  c, \
-	  cntx  \
-	); \
+	/* Only proceed with an induced method if all operands have the same
+	   (complex) datatype. If any datatypes differ, skip the induced method
+	   chooser function and proceed directly with native execution, which is
+	   where mixed datatype support will be implemented (if at all). */ \
+	if ( bli_obj_dt( a ) == bli_obj_dt( c ) && \
+	     bli_obj_is_complex( c ) ) \
+	{ \
+		/* Invoke the operation's "ind" function--its induced method front-end.
+		   For complex problems, it calls the highest priority induced method
+		   that is available (ie: implemented and enabled), and if none are
+		   enabled, it calls native execution. (For real problems, it calls
+		   the operation's native execution interface.) */ \
+		PASTEMAC(opname,ind)( alpha, a, beta, c, cntx ); \
+	} \
+	else \
+	{ \
+		PASTEMAC(opname,nat)( alpha, a, beta, c, cntx ); \
+	} \
 }
 
 GENFRONT( herk )
@@ -159,14 +183,24 @@ void PASTEMAC(opname,EX_SUF) \
 \
 	BLIS_OAPI_CNTX_DECL \
 \
-	PASTEMAC(opname,ind) \
-	( \
-	  side, \
-	  alpha, \
-	  a, \
-	  b, \
-	  cntx  \
-	); \
+	/* Only proceed with an induced method if all operands have the same
+	   (complex) datatype. If any datatypes differ, skip the induced method
+	   chooser function and proceed directly with native execution, which is
+	   where mixed datatype support will be implemented (if at all). */ \
+	if ( bli_obj_dt( a ) == bli_obj_dt( b ) && \
+	     bli_obj_is_complex( b ) ) \
+	{ \
+		/* Invoke the operation's "ind" function--its induced method front-end.
+		   For complex problems, it calls the highest priority induced method
+		   that is available (ie: implemented and enabled), and if none are
+		   enabled, it calls native execution. (For real problems, it calls
+		   the operation's native execution interface.) */ \
+		PASTEMAC(opname,ind)( side, alpha, a, b, cntx ); \
+	} \
+	else \
+	{ \
+		PASTEMAC(opname,nat)( side, alpha, a, b, cntx ); \
+	} \
 }
 
 GENFRONT( trmm )
diff --git a/frame/3/gemm/bli_gemm_cntl.c b/frame/3/gemm/bli_gemm_cntl.c
index b17ce10ac..3e13f23fa 100644
--- a/frame/3/gemm/bli_gemm_cntl.c
+++ b/frame/3/gemm/bli_gemm_cntl.c
@@ -36,17 +36,21 @@
 
 cntl_t* bli_gemm_cntl_create
      (
-       opid_t family
+       opid_t family,
+       pack_t schema_a,
+       pack_t schema_b
      )
 {
-	return bli_gemmbp_cntl_create( family );
+	return bli_gemmbp_cntl_create( family, schema_a, schema_b );
 }
 
 // -----------------------------------------------------------------------------
 
 cntl_t* bli_gemmbp_cntl_create
      (
-       opid_t family
+       opid_t family,
+       pack_t schema_a,
+       pack_t schema_b
      )
 {
 	void* macro_kernel_p = bli_gemm_ker_var2;
@@ -82,7 +86,7 @@ cntl_t* bli_gemmbp_cntl_create
 	  FALSE,   // do NOT invert diagonal
 	  FALSE,   // reverse iteration if upper?
 	  FALSE,   // reverse iteration if lower?
-	  BLIS_PACKED_ROW_PANELS,
+	  schema_a, // normally BLIS_PACKED_ROW_PANELS
 	  BLIS_BUFFER_FOR_A_BLOCK,
 	  gemm_cntl_bp_bu
 	);
@@ -106,7 +110,7 @@ cntl_t* bli_gemmbp_cntl_create
 	  FALSE,   // do NOT invert diagonal
 	  FALSE,   // reverse iteration if upper?
 	  FALSE,   // reverse iteration if lower?
-	  BLIS_PACKED_COL_PANELS,
+	  schema_b, // normally BLIS_PACKED_COL_PANELS
 	  BLIS_BUFFER_FOR_B_PANEL,
 	  gemm_cntl_op_bp
 	);
@@ -134,6 +138,10 @@ cntl_t* bli_gemmbp_cntl_create
 
 // -----------------------------------------------------------------------------
 
+// This control tree creation function is disabled because it is no longer used.
+// (It was originally created in the run up to publishing the 1m journal article,
+// but was disabled to reduce complexity.)
+#if 0
 cntl_t* bli_gemmpb_cntl_create
      (
        opid_t family
@@ -223,6 +231,7 @@ cntl_t* bli_gemmpb_cntl_create
 
 	return gemm_cntl_vl_mm;
 }
+#endif
 
 // -----------------------------------------------------------------------------
 
diff --git a/frame/3/gemm/bli_gemm_cntl.h b/frame/3/gemm/bli_gemm_cntl.h
index 3b643e1fc..3b3cb1cf2 100644
--- a/frame/3/gemm/bli_gemm_cntl.h
+++ b/frame/3/gemm/bli_gemm_cntl.h
@@ -34,20 +34,26 @@
 
 cntl_t* bli_gemm_cntl_create
      (
-       opid_t family
+       opid_t family,
+       pack_t schema_a,
+       pack_t schema_b
      );
 
 // -----------------------------------------------------------------------------
 
 cntl_t* bli_gemmbp_cntl_create
      (
-       opid_t family
+       opid_t family,
+       pack_t schema_a,
+       pack_t schema_b
      );
 
+#if 0
 cntl_t* bli_gemmpb_cntl_create
      (
-       opid_t family
+       opid_t family,
      );
+#endif
 
 // -----------------------------------------------------------------------------
 
diff --git a/frame/3/gemm/bli_gemm_front.c b/frame/3/gemm/bli_gemm_front.c
index f2600d791..8aae5b476 100644
--- a/frame/3/gemm/bli_gemm_front.c
+++ b/frame/3/gemm/bli_gemm_front.c
@@ -87,10 +87,34 @@ void bli_gemm_front
 	}
 
 	// Record the threading for each level within the context.
-	bli_cntx_set_thrloop_from_env( BLIS_GEMM, BLIS_LEFT, cntx,
-	                               bli_obj_length( &c_local ),
-	                               bli_obj_width( &c_local ),
-	                               bli_obj_width( &a_local ) );
+	bli_cntx_set_thrloop_from_env
+	(
+	  BLIS_GEMM,
+	  BLIS_LEFT, // ignored for gemm/hemm/symm
+	  bli_obj_length( &c_local ),
+	  bli_obj_width( &c_local ),
+	  bli_obj_width( &a_local ),
+	  cntx
+	);
+
+	// A sort of hack for communicating the desired pach schemas for A and B
+	// to bli_gemm_cntl_create() (via bli_l3_thread_decorator() and
+	// bli_l3_cntl_create_if()). This allows us to access the schemas from
+	// the control tree, which hopefully reduces some confusion, particularly
+	// in bli_packm_init().
+	if ( bli_cntx_method( cntx ) == BLIS_NAT )
+	{
+		bli_obj_set_pack_schema( BLIS_PACKED_ROW_PANELS, &a_local );
+		bli_obj_set_pack_schema( BLIS_PACKED_COL_PANELS, &b_local );
+	}
+	else // if ( bli_cntx_method( cntx ) != BLIS_NAT )
+	{
+		pack_t schema_a = bli_cntx_schema_a_block( cntx );
+		pack_t schema_b = bli_cntx_schema_b_panel( cntx );
+
+		bli_obj_set_pack_schema( schema_a, &a_local );
+		bli_obj_set_pack_schema( schema_b, &b_local );
+	}
 
 	// Invoke the internal back-end via the thread handler.
 	bli_l3_thread_decorator
diff --git a/frame/3/hemm/bli_hemm_front.c b/frame/3/hemm/bli_hemm_front.c
index 2406ee1d5..b12424d63 100644
--- a/frame/3/hemm/bli_hemm_front.c
+++ b/frame/3/hemm/bli_hemm_front.c
@@ -88,10 +88,34 @@ void bli_hemm_front
 	}
 
 	// Record the threading for each level within the context.
-	bli_cntx_set_thrloop_from_env( BLIS_HEMM, BLIS_LEFT, cntx,
-                                   bli_obj_length( &c_local ),
-                                   bli_obj_width( &c_local ),
-                                   bli_obj_width( &a_local ) );
+	bli_cntx_set_thrloop_from_env
+	(
+	  BLIS_HEMM,
+	  BLIS_LEFT, // ignored for gemm/hemm/symm
+	  bli_obj_length( &c_local ),
+	  bli_obj_width( &c_local ),
+	  bli_obj_width( &a_local ),
+	  cntx
+	);
+
+	// A sort of hack for communicating the desired pach schemas for A and B
+	// to bli_gemm_cntl_create() (via bli_l3_thread_decorator() and
+	// bli_l3_cntl_create_if()). This allows us to access the schemas from
+	// the control tree, which hopefully reduces some confusion, particularly
+	// in bli_packm_init().
+	if ( bli_cntx_method( cntx ) == BLIS_NAT )
+	{
+		bli_obj_set_pack_schema( BLIS_PACKED_ROW_PANELS, &a_local );
+		bli_obj_set_pack_schema( BLIS_PACKED_COL_PANELS, &b_local );
+	}
+	else // if ( bli_cntx_method( cntx ) != BLIS_NAT )
+	{
+		pack_t schema_a = bli_cntx_schema_a_block( cntx );
+		pack_t schema_b = bli_cntx_schema_b_panel( cntx );
+
+		bli_obj_set_pack_schema( schema_a, &a_local );
+		bli_obj_set_pack_schema( schema_b, &b_local );
+	}
 
 	// Invoke the internal back-end.
 	bli_l3_thread_decorator
diff --git a/frame/3/her2k/bli_her2k_front.c b/frame/3/her2k/bli_her2k_front.c
index 9448b881e..15ee65fad 100644
--- a/frame/3/her2k/bli_her2k_front.c
+++ b/frame/3/her2k/bli_her2k_front.c
@@ -106,10 +106,38 @@ void bli_her2k_front
 	}
 
 	// Record the threading for each level within the context.
-	bli_cntx_set_thrloop_from_env( BLIS_HER2K, BLIS_LEFT, cntx,
-                                   bli_obj_length( &c_local ),
-                                   bli_obj_width( &c_local ),
-                                   bli_obj_width( &a_local ) );
+	bli_cntx_set_thrloop_from_env
+	(
+	  BLIS_HER2K,
+	  BLIS_LEFT, // ignored for her[2]k/syr[2]k
+	  bli_obj_length( &c_local ),
+	  bli_obj_width( &c_local ),
+	  bli_obj_width( &a_local ),
+	  cntx
+	);
+
+	// A sort of hack for communicating the desired pach schemas for A and B
+	// to bli_gemm_cntl_create() (via bli_l3_thread_decorator() and
+	// bli_l3_cntl_create_if()). This allows us to access the schemas from
+	// the control tree, which hopefully reduces some confusion, particularly
+	// in bli_packm_init().
+	if ( bli_cntx_method( cntx ) == BLIS_NAT )
+	{
+		bli_obj_set_pack_schema( BLIS_PACKED_ROW_PANELS, &a_local );
+		bli_obj_set_pack_schema( BLIS_PACKED_COL_PANELS, &bh_local );
+		bli_obj_set_pack_schema( BLIS_PACKED_ROW_PANELS, &b_local );
+		bli_obj_set_pack_schema( BLIS_PACKED_COL_PANELS, &ah_local );
+	}
+	else // if ( bli_cntx_method( cntx ) != BLIS_NAT )
+	{
+		pack_t schema_a = bli_cntx_schema_a_block( cntx );
+		pack_t schema_b = bli_cntx_schema_b_panel( cntx );
+
+		bli_obj_set_pack_schema( schema_a, &a_local );
+		bli_obj_set_pack_schema( schema_b, &bh_local );
+		bli_obj_set_pack_schema( schema_a, &b_local );
+		bli_obj_set_pack_schema( schema_b, &ah_local );
+	}
 
 	// Invoke herk twice, using beta only the first time.
 
diff --git a/frame/3/herk/bli_herk_front.c b/frame/3/herk/bli_herk_front.c
index 8b2379a66..f6e5b55a3 100644
--- a/frame/3/herk/bli_herk_front.c
+++ b/frame/3/herk/bli_herk_front.c
@@ -86,10 +86,34 @@ void bli_herk_front
 	}
 
 	// Record the threading for each level within the context.
-	bli_cntx_set_thrloop_from_env( BLIS_HERK, BLIS_LEFT, cntx,
-                                   bli_obj_length( &c_local ),
-                                   bli_obj_width( &c_local ),
-                                   bli_obj_width( &a_local ) );
+	bli_cntx_set_thrloop_from_env
+	(
+	  BLIS_HERK,
+	  BLIS_LEFT, // ignored for her[2]k/syr[2]k
+	  bli_obj_length( &c_local ),
+	  bli_obj_width( &c_local ),
+	  bli_obj_width( &a_local ),
+	  cntx
+	);
+
+	// A sort of hack for communicating the desired pach schemas for A and B
+	// to bli_gemm_cntl_create() (via bli_l3_thread_decorator() and
+	// bli_l3_cntl_create_if()). This allows us to access the schemas from
+	// the control tree, which hopefully reduces some confusion, particularly
+	// in bli_packm_init().
+	if ( bli_cntx_method( cntx ) == BLIS_NAT )
+	{
+		bli_obj_set_pack_schema( BLIS_PACKED_ROW_PANELS, &a_local );
+		bli_obj_set_pack_schema( BLIS_PACKED_COL_PANELS, &ah_local );
+	}
+	else // if ( bli_cntx_method( cntx ) != BLIS_NAT )
+	{
+		pack_t schema_a = bli_cntx_schema_a_block( cntx );
+		pack_t schema_b = bli_cntx_schema_b_panel( cntx );
+
+		bli_obj_set_pack_schema( schema_a, &a_local );
+		bli_obj_set_pack_schema( schema_b, &ah_local );
+	}
 
 	// Invoke the internal back-end.
 	bli_l3_thread_decorator
diff --git a/frame/3/symm/bli_symm_front.c b/frame/3/symm/bli_symm_front.c
index 0c229ef9b..84263bc9d 100644
--- a/frame/3/symm/bli_symm_front.c
+++ b/frame/3/symm/bli_symm_front.c
@@ -87,10 +87,34 @@ void bli_symm_front
 	}
 
 	// Record the threading for each level within the context.
-	bli_cntx_set_thrloop_from_env( BLIS_SYMM, BLIS_LEFT, cntx,
-                                   bli_obj_length( &c_local ),
-                                   bli_obj_width( &c_local ),
-                                   bli_obj_width( &a_local ) );
+	bli_cntx_set_thrloop_from_env
+	(
+	  BLIS_SYMM,
+	  BLIS_LEFT, // ignored for gemm/hemm/symm
+	  bli_obj_length( &c_local ),
+	  bli_obj_width( &c_local ),
+	  bli_obj_width( &a_local ),
+	  cntx
+	);
+
+	// A sort of hack for communicating the desired pach schemas for A and B
+	// to bli_gemm_cntl_create() (via bli_l3_thread_decorator() and
+	// bli_l3_cntl_create_if()). This allows us to access the schemas from
+	// the control tree, which hopefully reduces some confusion, particularly
+	// in bli_packm_init().
+	if ( bli_cntx_method( cntx ) == BLIS_NAT )
+	{
+		bli_obj_set_pack_schema( BLIS_PACKED_ROW_PANELS, &a_local );
+		bli_obj_set_pack_schema( BLIS_PACKED_COL_PANELS, &b_local );
+	}
+	else // if ( bli_cntx_method( cntx ) != BLIS_NAT )
+	{
+		pack_t schema_a = bli_cntx_schema_a_block( cntx );
+		pack_t schema_b = bli_cntx_schema_b_panel( cntx );
+
+		bli_obj_set_pack_schema( schema_a, &a_local );
+		bli_obj_set_pack_schema( schema_b, &b_local );
+	}
 
 	// Invoke the internal back-end.
 	bli_l3_thread_decorator
diff --git a/frame/3/syr2k/bli_syr2k_front.c b/frame/3/syr2k/bli_syr2k_front.c
index 32981cb89..769ca56a0 100644
--- a/frame/3/syr2k/bli_syr2k_front.c
+++ b/frame/3/syr2k/bli_syr2k_front.c
@@ -87,10 +87,38 @@ void bli_syr2k_front
 	}
 
 	// Record the threading for each level within the context.
-	bli_cntx_set_thrloop_from_env( BLIS_SYR2K, BLIS_LEFT, cntx,
-                                   bli_obj_length( &c_local ),
-                                   bli_obj_width( &c_local ),
-                                   bli_obj_width( &a_local ) );
+	bli_cntx_set_thrloop_from_env
+	(
+	  BLIS_SYR2K,
+	  BLIS_LEFT, // ignored for her[2]k/syr[2]k
+	  bli_obj_length( &c_local ),
+	  bli_obj_width( &c_local ),
+	  bli_obj_width( &a_local ),
+	  cntx
+	);
+
+	// A sort of hack for communicating the desired pach schemas for A and B
+	// to bli_gemm_cntl_create() (via bli_l3_thread_decorator() and
+	// bli_l3_cntl_create_if()). This allows us to access the schemas from
+	// the control tree, which hopefully reduces some confusion, particularly
+	// in bli_packm_init().
+	if ( bli_cntx_method( cntx ) == BLIS_NAT )
+	{
+		bli_obj_set_pack_schema( BLIS_PACKED_ROW_PANELS, &a_local );
+		bli_obj_set_pack_schema( BLIS_PACKED_COL_PANELS, &bt_local );
+		bli_obj_set_pack_schema( BLIS_PACKED_ROW_PANELS, &b_local );
+		bli_obj_set_pack_schema( BLIS_PACKED_COL_PANELS, &at_local );
+	}
+	else // if ( bli_cntx_method( cntx ) != BLIS_NAT )
+	{
+		pack_t schema_a = bli_cntx_schema_a_block( cntx );
+		pack_t schema_b = bli_cntx_schema_b_panel( cntx );
+
+		bli_obj_set_pack_schema( schema_a, &a_local );
+		bli_obj_set_pack_schema( schema_b, &bt_local );
+		bli_obj_set_pack_schema( schema_a, &b_local );
+		bli_obj_set_pack_schema( schema_b, &at_local );
+	}
 
 	// Invoke herk twice, using beta only the first time.
 
diff --git a/frame/3/syrk/bli_syrk_front.c b/frame/3/syrk/bli_syrk_front.c
index eed5f0ebc..7a66ad68a 100644
--- a/frame/3/syrk/bli_syrk_front.c
+++ b/frame/3/syrk/bli_syrk_front.c
@@ -80,10 +80,34 @@ void bli_syrk_front
 	}
 
 	// Record the threading for each level within the context.
-	bli_cntx_set_thrloop_from_env( BLIS_SYRK, BLIS_LEFT, cntx,
-                                   bli_obj_length( &c_local ),
-                                   bli_obj_width( &c_local ),
-                                   bli_obj_width( &a_local ) );
+	bli_cntx_set_thrloop_from_env
+	(
+	  BLIS_SYRK,
+	  BLIS_LEFT, // ignored for her[2]k/syr[2]k
+	  bli_obj_length( &c_local ),
+	  bli_obj_width( &c_local ),
+	  bli_obj_width( &a_local ),
+	  cntx
+	);
+
+	// A sort of hack for communicating the desired pach schemas for A and B
+	// to bli_gemm_cntl_create() (via bli_l3_thread_decorator() and
+	// bli_l3_cntl_create_if()). This allows us to access the schemas from
+	// the control tree, which hopefully reduces some confusion, particularly
+	// in bli_packm_init().
+	if ( bli_cntx_method( cntx ) == BLIS_NAT )
+	{
+		bli_obj_set_pack_schema( BLIS_PACKED_ROW_PANELS, &a_local );
+		bli_obj_set_pack_schema( BLIS_PACKED_COL_PANELS, &at_local );
+	}
+	else // if ( bli_cntx_method( cntx ) != BLIS_NAT )
+	{
+		pack_t schema_a = bli_cntx_schema_a_block( cntx );
+		pack_t schema_b = bli_cntx_schema_b_panel( cntx );
+
+		bli_obj_set_pack_schema( schema_a, &a_local );
+		bli_obj_set_pack_schema( schema_b, &at_local );
+	}
 
 	// Invoke the internal back-end.
 	bli_l3_thread_decorator
diff --git a/frame/3/trmm/bli_trmm_front.c b/frame/3/trmm/bli_trmm_front.c
index afdabbbd2..935972442 100644
--- a/frame/3/trmm/bli_trmm_front.c
+++ b/frame/3/trmm/bli_trmm_front.c
@@ -130,10 +130,34 @@ void bli_trmm_front
 	bli_obj_set_as_root( &c_local );
 
 	// Record the threading for each level within the context.
-	bli_cntx_set_thrloop_from_env( BLIS_TRMM, side, cntx,
-                                   bli_obj_length( &c_local ),
-                                   bli_obj_width( &c_local ),
-                                   bli_obj_width( &a_local ) );
+	bli_cntx_set_thrloop_from_env
+	(
+	  BLIS_TRMM,
+	  side,
+	  bli_obj_length( &c_local ),
+	  bli_obj_width( &c_local ),
+	  bli_obj_width( &a_local ),
+	  cntx
+	);
+
+	// A sort of hack for communicating the desired pach schemas for A and B
+	// to bli_gemm_cntl_create() (via bli_l3_thread_decorator() and
+	// bli_l3_cntl_create_if()). This allows us to access the schemas from
+	// the control tree, which hopefully reduces some confusion, particularly
+	// in bli_packm_init().
+	if ( bli_cntx_method( cntx ) == BLIS_NAT )
+	{
+		bli_obj_set_pack_schema( BLIS_PACKED_ROW_PANELS, &a_local );
+		bli_obj_set_pack_schema( BLIS_PACKED_COL_PANELS, &b_local );
+	}
+	else // if ( bli_cntx_method( cntx ) != BLIS_NAT )
+	{
+		pack_t schema_a = bli_cntx_schema_a_block( cntx );
+		pack_t schema_b = bli_cntx_schema_b_panel( cntx );
+
+		bli_obj_set_pack_schema( schema_a, &a_local );
+		bli_obj_set_pack_schema( schema_b, &b_local );
+	}
 
 	// Invoke the internal back-end.
 	bli_l3_thread_decorator
diff --git a/frame/3/trmm3/bli_trmm3_front.c b/frame/3/trmm3/bli_trmm3_front.c
index 664a7fd51..0f772f0fb 100644
--- a/frame/3/trmm3/bli_trmm3_front.c
+++ b/frame/3/trmm3/bli_trmm3_front.c
@@ -129,10 +129,34 @@ void bli_trmm3_front
 	bli_obj_set_as_root( &c_local );
 
 	// Record the threading for each level within the context.
-	bli_cntx_set_thrloop_from_env( BLIS_TRMM3, side, cntx,
-                                   bli_obj_length( &c_local ),
-                                   bli_obj_width( &c_local ),
-                                   bli_obj_width( &a_local ) );
+	bli_cntx_set_thrloop_from_env
+	(
+	  BLIS_TRMM3,
+	  side,
+	  bli_obj_length( &c_local ),
+	  bli_obj_width( &c_local ),
+	  bli_obj_width( &a_local ),
+	  cntx
+	);
+
+	// A sort of hack for communicating the desired pach schemas for A and B
+	// to bli_gemm_cntl_create() (via bli_l3_thread_decorator() and
+	// bli_l3_cntl_create_if()). This allows us to access the schemas from
+	// the control tree, which hopefully reduces some confusion, particularly
+	// in bli_packm_init().
+	if ( bli_cntx_method( cntx ) == BLIS_NAT )
+	{
+		bli_obj_set_pack_schema( BLIS_PACKED_ROW_PANELS, &a_local );
+		bli_obj_set_pack_schema( BLIS_PACKED_COL_PANELS, &b_local );
+	}
+	else // if ( bli_cntx_method( cntx ) != BLIS_NAT )
+	{
+		pack_t schema_a = bli_cntx_schema_a_block( cntx );
+		pack_t schema_b = bli_cntx_schema_b_panel( cntx );
+
+		bli_obj_set_pack_schema( schema_a, &a_local );
+		bli_obj_set_pack_schema( schema_b, &b_local );
+	}
 
 	// Invoke the internal back-end.
 	bli_l3_thread_decorator
diff --git a/frame/3/trsm/bli_trsm_cntl.c b/frame/3/trsm/bli_trsm_cntl.c
index e05fc3d20..df9b831a3 100644
--- a/frame/3/trsm/bli_trsm_cntl.c
+++ b/frame/3/trsm/bli_trsm_cntl.c
@@ -36,16 +36,21 @@
 
 cntl_t* bli_trsm_cntl_create
      (
-       side_t side
+       side_t side,
+       pack_t schema_a,
+       pack_t schema_b
      )
 {
-	if ( bli_is_left( side ) ) return bli_trsm_l_cntl_create();
-	else                       return bli_trsm_r_cntl_create();
+	if ( bli_is_left( side ) )
+		return bli_trsm_l_cntl_create( schema_a, schema_b );
+	else
+		return bli_trsm_r_cntl_create( schema_a, schema_b );
 }
 
 cntl_t* bli_trsm_l_cntl_create
      (
-       void
+       pack_t schema_a,
+       pack_t schema_b
      )
 {
 	void* macro_kernel_p = bli_trsm_xx_ker_var2;
@@ -79,7 +84,7 @@ cntl_t* bli_trsm_l_cntl_create
 	  TRUE,    // do NOT invert diagonal
 	  TRUE,    // reverse iteration if upper?
 	  FALSE,   // reverse iteration if lower?
-	  BLIS_PACKED_ROW_PANELS,
+	  schema_a, // normally BLIS_PACKED_ROW_PANELS
 	  BLIS_BUFFER_FOR_A_BLOCK,
 	  trsm_cntl_bp_bu
 	);
@@ -103,7 +108,7 @@ cntl_t* bli_trsm_l_cntl_create
 	  FALSE,   // do NOT invert diagonal
 	  FALSE,   // reverse iteration if upper?
 	  FALSE,   // reverse iteration if lower?
-	  BLIS_PACKED_COL_PANELS,
+	  schema_b, // normally BLIS_PACKED_COL_PANELS
 	  BLIS_BUFFER_FOR_B_PANEL,
 	  trsm_cntl_op_bp
 	);
@@ -131,7 +136,8 @@ cntl_t* bli_trsm_l_cntl_create
 
 cntl_t* bli_trsm_r_cntl_create
      (
-       void
+       pack_t schema_a,
+       pack_t schema_b
      )
 {
 	void* macro_kernel_p = bli_trsm_xx_ker_var2;
@@ -165,7 +171,7 @@ cntl_t* bli_trsm_r_cntl_create
 	  FALSE,   // do NOT invert diagonal
 	  FALSE,   // reverse iteration if upper?
 	  FALSE,   // reverse iteration if lower?
-	  BLIS_PACKED_ROW_PANELS,
+	  schema_a, // normally BLIS_PACKED_ROW_PANELS
 	  BLIS_BUFFER_FOR_A_BLOCK,
 	  trsm_cntl_bp_bu
 	);
@@ -189,7 +195,7 @@ cntl_t* bli_trsm_r_cntl_create
 	  TRUE,    // do NOT invert diagonal
 	  FALSE,   // reverse iteration if upper?
 	  TRUE,    // reverse iteration if lower?
-	  BLIS_PACKED_COL_PANELS,
+	  schema_b, // normally BLIS_PACKED_COL_PANELS
 	  BLIS_BUFFER_FOR_B_PANEL,
 	  trsm_cntl_op_bp
 	);
diff --git a/frame/3/trsm/bli_trsm_cntl.h b/frame/3/trsm/bli_trsm_cntl.h
index cfd20cad3..77c36aec2 100644
--- a/frame/3/trsm/bli_trsm_cntl.h
+++ b/frame/3/trsm/bli_trsm_cntl.h
@@ -34,17 +34,21 @@
 
 cntl_t* bli_trsm_cntl_create
      (
-       side_t side
+       side_t side,
+       pack_t schema_a,
+       pack_t schema_b
      );
 
 cntl_t* bli_trsm_l_cntl_create
      (
-       void
+       pack_t schema_a,
+       pack_t schema_b
      );
 
 cntl_t* bli_trsm_r_cntl_create
      (
-       void
+       pack_t schema_a,
+       pack_t schema_b
      );
 
 void bli_trsm_cntl_free
diff --git a/frame/3/trsm/bli_trsm_front.c b/frame/3/trsm/bli_trsm_front.c
index 2bc6d0186..081a2c284 100644
--- a/frame/3/trsm/bli_trsm_front.c
+++ b/frame/3/trsm/bli_trsm_front.c
@@ -121,10 +121,34 @@ void bli_trsm_front
 	bli_obj_set_as_root( &c_local );
 
 	// Record the threading for each level within the context.
-	bli_cntx_set_thrloop_from_env( BLIS_TRSM, side, cntx,
-                                   bli_obj_length( &c_local ),
-                                   bli_obj_width( &c_local ),
-                                   bli_obj_width( &a_local ) );
+	bli_cntx_set_thrloop_from_env
+	(
+	  BLIS_TRSM,
+	  side,
+	  bli_obj_length( &c_local ),
+	  bli_obj_width( &c_local ),
+	  bli_obj_width( &a_local ),
+	  cntx
+	);
+
+	// A sort of hack for communicating the desired pach schemas for A and B
+	// to bli_trsm_cntl_create() (via bli_l3_thread_decorator() and
+	// bli_l3_cntl_create_if()). This allows us to access the schemas from
+	// the control tree, which hopefully reduces some confusion, particularly
+	// in bli_packm_init().
+	if ( bli_cntx_method( cntx ) == BLIS_NAT )
+	{
+		bli_obj_set_pack_schema( BLIS_PACKED_ROW_PANELS, &a_local );
+		bli_obj_set_pack_schema( BLIS_PACKED_COL_PANELS, &b_local );
+	}
+	else // if ( bli_cntx_method( cntx ) != BLIS_NAT )
+	{
+		pack_t schema_a = bli_cntx_schema_a_block( cntx );
+		pack_t schema_b = bli_cntx_schema_b_panel( cntx );
+
+		bli_obj_set_pack_schema( schema_a, &a_local );
+		bli_obj_set_pack_schema( schema_b, &b_local );
+	}
 
 	// Invoke the internal back-end.
 	bli_l3_thread_decorator
diff --git a/frame/base/bli_cntx.c b/frame/base/bli_cntx.c
index 981b01c3e..d36a20ded 100644
--- a/frame/base/bli_cntx.c
+++ b/frame/base/bli_cntx.c
@@ -869,10 +869,10 @@ void bli_cntx_set_thrloop_from_env
      (
        opid_t  l3_op,
        side_t  side,
-       cntx_t* cntx,
        dim_t   m,
        dim_t   n,
-       dim_t   k
+       dim_t   k,
+       cntx_t* cntx
      )
 {
 	dim_t jc, pc, ic, jr, ir;
@@ -988,7 +988,7 @@ void bli_cntx_set_thrloop_from_env
 			);
 		}
 	}
-	else // if ( l3_op == BLIS_GEMM || l3_op == BLIS_HERK )
+	else // any other level-3 operation besides trmm/trsm
 	{
 		bli_cntx_set_thrloop
 		(
diff --git a/frame/base/bli_cntx.h b/frame/base/bli_cntx.h
index ac43312bc..4aaec97c4 100644
--- a/frame/base/bli_cntx.h
+++ b/frame/base/bli_cntx.h
@@ -674,12 +674,15 @@ void  bli_cntx_set_l1f_kers( dim_t n_kers, ... );
 void  bli_cntx_set_l1v_kers( dim_t n_kers, ... );
 void  bli_cntx_set_packm_kers( dim_t n_kers, ... );
 
-void  bli_cntx_set_thrloop_from_env( opid_t  l3_op,
-                                     side_t  side,
-                                     cntx_t* cntx,
-                                     dim_t m,
-                                     dim_t n,
-                                     dim_t k );
+void  bli_cntx_set_thrloop_from_env
+     (
+       opid_t  l3_op,
+       side_t  side,
+       dim_t   m,
+       dim_t   n,
+       dim_t   k,
+       cntx_t* cntx
+     );
 
 void  bli_cntx_print( cntx_t* cntx );
 
diff --git a/frame/thread/bli_thrcomm_openmp.c b/frame/thread/bli_thrcomm_openmp.c
index 131f70973..f2197597f 100644
--- a/frame/thread/bli_thrcomm_openmp.c
+++ b/frame/thread/bli_thrcomm_openmp.c
@@ -231,11 +231,18 @@ void bli_l3_thread_decorator
 	{
 		dim_t      id = omp_get_thread_num();
 
+		obj_t      a_t, b_t, c_t;
 		cntl_t*    cntl_use;
 		thrinfo_t* thread;
 
+		// Alias thread-local copies of A, B, and C. These will be the objects
+		// we pass into the thread functions.
+		bli_obj_alias_to( a, &a_t );
+		bli_obj_alias_to( b, &b_t );
+		bli_obj_alias_to( c, &c_t );
+
 		// Create a default control tree for the operation, if needed.
-		bli_l3_cntl_create_if( family, a, b, c, cntl, &cntl_use );
+		bli_l3_cntl_create_if( family, &a_t, &b_t, &c_t, cntl, &cntl_use );
 
 		// Create the root node of the current thread's thrinfo_t structure.
 		bli_l3_thrinfo_create_root( id, gl_comm, cntx, cntl_use, &thread );
@@ -243,17 +250,17 @@ void bli_l3_thread_decorator
 		func
 		(
 		  alpha,
-		  a,
-		  b,
+		  &a_t,
+		  &b_t,
 		  beta,
-		  c,
+		  &c_t,
 		  cntx,
 		  cntl_use,
 		  thread
 		);
 
 		// Free the control tree, if one was created locally.
-		bli_l3_cntl_free_if( a, b, c, cntl, cntl_use, thread );
+		bli_l3_cntl_free_if( &a_t, &b_t, &c_t, cntl, cntl_use, thread );
 
 #ifdef PRINT_THRINFO
 		threads[id] = thread;
diff --git a/frame/thread/bli_thrcomm_pthreads.c b/frame/thread/bli_thrcomm_pthreads.c
index e2fa35c35..132fb6740 100644
--- a/frame/thread/bli_thrcomm_pthreads.c
+++ b/frame/thread/bli_thrcomm_pthreads.c
@@ -161,11 +161,18 @@ void* bli_l3_thread_entry( void* data_void )
 	dim_t          id       = data->id;
 	thrcomm_t*     gl_comm  = data->gl_comm;
 
+	obj_t          a_t, b_t, c_t;
 	cntl_t*        cntl_use;
 	thrinfo_t*     thread;
 
+	// Alias thread-local copies of A, B, and C. These will be the objects
+	// we pass into the thread function.
+	bli_obj_alias_to( a, &a_t );
+	bli_obj_alias_to( b, &b_t );
+	bli_obj_alias_to( c, &c_t );
+
 	// Create a default control tree for the operation, if needed.
-	bli_l3_cntl_create_if( family, a, b, c, cntl, &cntl_use );
+	bli_l3_cntl_create_if( family, &a_t, &b_t, &c_t, cntl, &cntl_use );
 
 	// Create the root node of the current thread's thrinfo_t structure.
 	bli_l3_thrinfo_create_root( id, gl_comm, cntx, cntl_use, &thread );
@@ -173,17 +180,17 @@ void* bli_l3_thread_entry( void* data_void )
 	func
 	(
 	  alpha,
-	  a,
-	  b,
+	  &a_t,
+	  &b_t,
 	  beta,
-	  c,
+	  &c_t,
 	  cntx,
 	  cntl_use,
 	  thread
 	);
 
 	// Free the control tree, if one was created locally.
-	bli_l3_cntl_free_if( a, b, c, cntl, cntl_use, thread );
+	bli_l3_cntl_free_if( &a_t, &b_t, &c_t, cntl, cntl_use, thread );
 
 	// Free the current thread's thrinfo_t structure.
 	bli_l3_thrinfo_free( thread );
diff --git a/frame/thread/bli_thrcomm_single.c b/frame/thread/bli_thrcomm_single.c
index cb0bc2ae4..068b7eda5 100644
--- a/frame/thread/bli_thrcomm_single.c
+++ b/frame/thread/bli_thrcomm_single.c
@@ -94,6 +94,12 @@ void bli_l3_thread_decorator
 	cntl_t*    cntl_use;
 	thrinfo_t* thread;
 
+	// NOTE: Unlike with the _openmp.c and _pthreads.c variants, we don't
+	// need to alias objects for A, B, and C since they were already aliased
+	// in bli_*_front(). (We only needed thread-local copies so each could
+	// safely reset their internal (beta) scalars on c after the first
+	// iteration of the pc (kc) loop.)
+
 	// Create a default control tree for the operation, if needed.
 	bli_l3_cntl_create_if( family, a, b, c, cntl, &cntl_use );