diff --git a/gtestsuite/testsuite/level3/trsm/ctrsm_generic.cpp b/gtestsuite/testsuite/level3/trsm/ctrsm_generic.cpp
index 0b8c35776..b0efde03e 100644
--- a/gtestsuite/testsuite/level3/trsm/ctrsm_generic.cpp
+++ b/gtestsuite/testsuite/level3/trsm/ctrsm_generic.cpp
@@ -80,7 +80,7 @@ TEST_P(ctrsmTest, RandomData) {
     char datatype   = std::get<10>(GetParam());
 
     // Set the threshold for the errors:
-    double thresh = 15*n*m*testinghelpers::getEpsilon<T>();
+    double thresh = std::max(m, n)*testinghelpers::getEpsilon<T>();
 
     //----------------------------------------------------------
     //     Call test body using these parameters
@@ -139,8 +139,8 @@ INSTANTIATE_TEST_SUITE_P(
             ::testing::Values('u','l'),                                      // uplo  u:upper, l:lower
             ::testing::Values('n','c','t'),                                  // transa
             ::testing::Values('n','u'),                                      // diaga , n=nonunit u=unit
-            ::testing::Range(gtint_t(10), gtint_t(11), 10),                  // m
-            ::testing::Range(gtint_t(10), gtint_t(11), 10),                  // n
+            ::testing::Range(gtint_t(10), gtint_t(31), 10),                  // m
+            ::testing::Range(gtint_t(10), gtint_t(31), 10),                  // n
             ::testing::Values(scomplex{2.0,-1.0}),                           // alpha
             ::testing::Values(gtint_t(0), gtint_t(3)),                       // increment to the leading dim of a
             ::testing::Values(gtint_t(0), gtint_t(4)),                       // increment to the leading dim of b
diff --git a/gtestsuite/testsuite/level3/trsm/dtrsm_generic.cpp b/gtestsuite/testsuite/level3/trsm/dtrsm_generic.cpp
index d15af9390..457828227 100644
--- a/gtestsuite/testsuite/level3/trsm/dtrsm_generic.cpp
+++ b/gtestsuite/testsuite/level3/trsm/dtrsm_generic.cpp
@@ -80,7 +80,7 @@ TEST_P(dtrsmTest, RandomData) {
     char datatype   = std::get<10>(GetParam());
 
     // Set the threshold for the errors:
-    double thresh = 20*n*m*testinghelpers::getEpsilon<T>();
+    double thresh = std::max(m, n)*testinghelpers::getEpsilon<T>();
 
     //----------------------------------------------------------
     //     Call test body using these parameters
diff --git a/gtestsuite/testsuite/level3/trsm/strsm_generic.cpp b/gtestsuite/testsuite/level3/trsm/strsm_generic.cpp
index 88c11b647..f4aadc4e3 100644
--- a/gtestsuite/testsuite/level3/trsm/strsm_generic.cpp
+++ b/gtestsuite/testsuite/level3/trsm/strsm_generic.cpp
@@ -80,7 +80,7 @@ TEST_P(strsmTest, RandomData) {
     char datatype   = std::get<10>(GetParam());
 
     // Set the threshold for the errors:
-    double thresh = 15*n*m*testinghelpers::getEpsilon<T>();
+    double thresh = std::max(m, n)*testinghelpers::getEpsilon<T>();
 
     //----------------------------------------------------------
     //     Call test body using these parameters
diff --git a/gtestsuite/testsuite/level3/trsm/test_trsm.h b/gtestsuite/testsuite/level3/trsm/test_trsm.h
index a42be916b..2cb13be5d 100644
--- a/gtestsuite/testsuite/level3/trsm/test_trsm.h
+++ b/gtestsuite/testsuite/level3/trsm/test_trsm.h
@@ -54,9 +54,17 @@ void test_trsm( char storage, char side, char uploa, char transa,
     //----------------------------------------------------------
     //        Initialize matrics with random values.
     //----------------------------------------------------------
-    std::vector<T> a = testinghelpers::get_random_matrix<T>(2, 18, storage, transa, mn, mn, lda, datatype);
-    std::vector<T> b = testinghelpers::get_random_matrix<T>(5, 12, storage, 'n', m, n, ldb, datatype);
+    gtint_t lower = (diaga = 'n')||(diaga = 'N') ? 3 : 0;
+    gtint_t upper = (diaga = 'n')||(diaga = 'N') ? 10 : 1;
+    std::vector<T> a = testinghelpers::get_random_matrix<T>(lower, upper, storage, transa, mn, mn, lda, datatype);
+    std::vector<T> b = testinghelpers::get_random_matrix<T>(3, 10, storage, 'n', m, n, ldb, datatype);
 
+    // Making A diagonally dominant so that the condition number is good and
+    // the algorithm doesn't diverge.
+    for (gtint_t i=0; i<mn; i++)
+    {
+        a[i+i*lda] = T{float(mn)}*a[i+i*lda];
+    }
     // Create a copy of v so that we can check reference results.
     std::vector<T> b_ref(b);
 
diff --git a/gtestsuite/testsuite/level3/trsm/ztrsm_generic.cpp b/gtestsuite/testsuite/level3/trsm/ztrsm_generic.cpp
index 8d16cbfd4..e0c1b4155 100644
--- a/gtestsuite/testsuite/level3/trsm/ztrsm_generic.cpp
+++ b/gtestsuite/testsuite/level3/trsm/ztrsm_generic.cpp
@@ -80,7 +80,7 @@ TEST_P(ztrsmTest, RandomData) {
     char datatype   = std::get<10>(GetParam());
 
     // Set the threshold for the errors:
-    double thresh = 15*n*m*testinghelpers::getEpsilon<T>();
+    double thresh = std::max(m, n)*testinghelpers::getEpsilon<T>();
 
     //----------------------------------------------------------
     //     Call test body using these parameters