diff --git a/examples/custom_criterion.cu b/examples/custom_criterion.cu
index 939d6ae..6d1dfb3 100644
--- a/examples/custom_criterion.cu
+++ b/examples/custom_criterion.cu
@@ -27,19 +27,12 @@
 // Inherit from the stopping_criterion class:
 class fixed_criterion final : public nvbench::stopping_criterion 
 {
-  nvbench::int64_t m_max_samples{};
   nvbench::int64_t m_num_samples{};
 
 public:
-  fixed_criterion() : nvbench::stopping_criterion{"fixed"} {}
-
-  // Setup the criterion in the `initialize()` method:
-  virtual void initialize(const nvbench::criterion_params &params) override 
-  {
-    m_params = params;
-    m_num_samples = 0;
-    m_max_samples = m_params.has_value("max-samples") ? m_params.get_int64("max-samples") : 42;
-  }
+  fixed_criterion()
+      : nvbench::stopping_criterion{"fixed", {{"max-samples", nvbench::int64_t{42}}}}
+  {}
 
   // Process new measurements in the `add_measurement()` method:
   virtual void add_measurement(nvbench::float64_t /* measurement */) override
@@ -50,16 +43,14 @@ public:
   // Check if the stopping criterion is met in the `is_finished()` method:
   virtual bool is_finished() override
   {
-    return m_num_samples >= m_max_samples;
+    return m_num_samples >= m_params.get_int64("max-samples");
   }
 
-  // Describe criterion parameters in the `get_params_description()` method:
-  virtual const params_description &get_params_description() const override
+protected:
+  // Setup the criterion in the `do_initialize()` method:
+  virtual void do_initialize() override 
   {
-    static const params_description desc{
-      {"max-samples", nvbench::named_values::type::int64}
-    };
-    return desc;
+    m_num_samples = 0;
   }
 };
 
diff --git a/nvbench/benchmark_base.cuh b/nvbench/benchmark_base.cuh
index efe0c83..55673b0 100644
--- a/nvbench/benchmark_base.cuh
+++ b/nvbench/benchmark_base.cuh
@@ -184,7 +184,10 @@ struct benchmark_base
 
   /// Accumulate at least this many seconds of timing data per measurement.
   /// Only applies to `stdrel` stopping criterion. @{
-  [[nodiscard]] nvbench::float64_t get_min_time() const { return m_criterion_params.get_float64("min-time"); }
+  [[nodiscard]] nvbench::float64_t get_min_time() const
+  {
+    return m_criterion_params.get_float64("min-time");
+  }
   benchmark_base &set_min_time(nvbench::float64_t min_time)
   {
     m_criterion_params.set_float64("min-time", min_time);
@@ -196,7 +199,10 @@ struct benchmark_base
   /// Noise is the relative standard deviation:
   /// `noise = stdev / mean_time`. 
   /// Only applies to `stdrel` stopping criterion. @{
-  [[nodiscard]] nvbench::float64_t get_max_noise() const { return m_criterion_params.get_float64("max-noise"); }
+  [[nodiscard]] nvbench::float64_t get_max_noise() const
+  {
+    return m_criterion_params.get_float64("max-noise");
+  }
   benchmark_base &set_max_noise(nvbench::float64_t max_noise)
   {
     m_criterion_params.set_float64("max-noise", max_noise);
diff --git a/nvbench/criterion_manager.cuh b/nvbench/criterion_manager.cuh
index 53206f5..e5c86ad 100644
--- a/nvbench/criterion_manager.cuh
+++ b/nvbench/criterion_manager.cuh
@@ -49,7 +49,8 @@ public:
   nvbench::stopping_criterion& get_criterion(const std::string& name);
   const nvbench::stopping_criterion& get_criterion(const std::string& name) const;
 
-  nvbench::stopping_criterion::params_description get_params_description() const;
+  using params_description = std::vector<std::pair<std::string, nvbench::named_values::type>>;
+  params_description get_params_description() const;
 };
 
 /**
diff --git a/nvbench/criterion_manager.cxx b/nvbench/criterion_manager.cxx
index 35d97f7..abf682c 100644
--- a/nvbench/criterion_manager.cxx
+++ b/nvbench/criterion_manager.cxx
@@ -69,25 +69,28 @@ stopping_criterion &criterion_manager::add(std::unique_ptr<stopping_criterion> c
   return *it->second.get();
 }
 
-nvbench::stopping_criterion::params_description criterion_manager::get_params_description() const
+nvbench::criterion_manager::params_description criterion_manager::get_params_description() const
 {
-  nvbench::stopping_criterion::params_description desc;
+  nvbench::criterion_manager::params_description desc;
 
   for (auto &[criterion_name, criterion] : m_map)
   {
-    for (auto param : criterion->get_params_description())
+    nvbench::criterion_params params = criterion->get_params();
+
+    for (auto param : params.get_names())
     {
+      nvbench::named_values::type type = params.get_type(param);
       if (std::find_if(desc.begin(), desc.end(), [&](auto d) {
-            return d.first == param.first && d.second != param.second;
+            return d.first == param && d.second != type;
           }) != desc.end())
       {
         NVBENCH_THROW(std::runtime_error,
                       "Stopping criterion \"{}\" parameter \"{}\" is already used by another "
                       "criterion with a different type.",
                       criterion_name,
-                      param.first);
+                      param);
       }
-      desc.push_back(param);
+      desc.emplace_back(param, type);
     }
   }
 
diff --git a/nvbench/detail/entropy_criterion.cuh b/nvbench/detail/entropy_criterion.cuh
index 2c143ab..e0a3763 100644
--- a/nvbench/detail/entropy_criterion.cuh
+++ b/nvbench/detail/entropy_criterion.cuh
@@ -29,10 +29,6 @@ namespace nvbench::detail
 
 class entropy_criterion final : public stopping_criterion
 {
-  // parameters
-  nvbench::float64_t m_max_angle{0.048};
-  nvbench::float64_t m_min_r2{0.36};
-
   // state
   nvbench::int64_t m_total_samples{};
   nvbench::float64_t m_total_cuda_time{};
@@ -49,10 +45,11 @@ class entropy_criterion final : public stopping_criterion
 public:
   entropy_criterion();
 
-  virtual void initialize(const criterion_params &params) override;
   virtual void add_measurement(nvbench::float64_t measurement) override;
   virtual bool is_finished() override;
-  virtual const params_description &get_params_description() const override;
+  
+protected:
+  virtual void do_initialize() override;
 };
 
 } // namespace nvbench::detail
diff --git a/nvbench/detail/entropy_criterion.cxx b/nvbench/detail/entropy_criterion.cxx
index 102b63e..c8ad16e 100644
--- a/nvbench/detail/entropy_criterion.cxx
+++ b/nvbench/detail/entropy_criterion.cxx
@@ -26,29 +26,19 @@ namespace nvbench::detail
 {
 
 entropy_criterion::entropy_criterion()
-  : stopping_criterion{"entropy"}
+    : stopping_criterion{"entropy",
+                         {{"max-angle", 0.048}, {"min-r2", 0.36}}}
 {
   m_freq_tracker.reserve(m_entropy_tracker.capacity() * 2);
   m_probabilities.reserve(m_entropy_tracker.capacity() * 2);
 }
 
-void entropy_criterion::initialize(const criterion_params &params)
+void entropy_criterion::do_initialize()
 {
-  m_params = params;
-  m_total_samples = 0;
+  m_total_samples   = 0;
   m_total_cuda_time = 0.0;
   m_entropy_tracker.clear();
   m_freq_tracker.clear();
-
-  if (m_params.has_value("max-angle"))
-  {
-    m_max_angle = m_params.get_float64("max-angle");
-  }
-
-  if (m_params.has_value("min-r2"))
-  {
-    m_min_r2 = m_params.get_float64("min-r2");
-  }
 }
 
 nvbench::float64_t entropy_criterion::compute_entropy() 
@@ -131,13 +121,13 @@ bool entropy_criterion::is_finished()
 
   const auto [slope, intercept] = statistics::compute_linear_regression(begin, end, mean);
 
-  if (statistics::slope2deg(slope) > m_max_angle) 
+  if (statistics::slope2deg(slope) > m_params.get_float64("max-angle")) 
   {
     return false;
   }
 
   const auto r2 = statistics::compute_r2(begin, end, mean, slope, intercept);
-  if (r2 < m_min_r2)
+  if (r2 < m_params.get_float64("min-r2"))
   {
     return false;
   }
@@ -145,13 +135,4 @@ bool entropy_criterion::is_finished()
   return true;
 }
 
-const entropy_criterion::params_description &entropy_criterion::get_params_description() const
-{
-  static const params_description desc{
-    {"max-angle", nvbench::named_values::type::float64},
-    {"min-r2", nvbench::named_values::type::float64},
-  };
-  return desc;
-}
-
 } // namespace nvbench::detail
diff --git a/nvbench/detail/stdrel_criterion.cuh b/nvbench/detail/stdrel_criterion.cuh
index c9bf6b6..d9d353c 100644
--- a/nvbench/detail/stdrel_criterion.cuh
+++ b/nvbench/detail/stdrel_criterion.cuh
@@ -29,10 +29,6 @@ namespace nvbench::detail
 
 class stdrel_criterion final : public stopping_criterion
 {
-  // parameters
-  nvbench::float64_t m_min_time{nvbench::detail::compat_min_time()};
-  nvbench::float64_t m_max_noise{nvbench::detail::compat_max_noise()}; 
-
   // state
   nvbench::int64_t m_total_samples{};
   nvbench::float64_t m_total_cuda_time{};
@@ -42,10 +38,11 @@ class stdrel_criterion final : public stopping_criterion
 public:
   stdrel_criterion();
 
-  virtual void initialize(const criterion_params &params) override;
   virtual void add_measurement(nvbench::float64_t measurement) override;
   virtual bool is_finished() override;
-  virtual const params_description &get_params_description() const override;
+
+protected:
+  virtual void do_initialize() override;
 };
 
 } // namespace nvbench::detail
diff --git a/nvbench/detail/stdrel_criterion.cxx b/nvbench/detail/stdrel_criterion.cxx
index 0c19282..a7a5d22 100644
--- a/nvbench/detail/stdrel_criterion.cxx
+++ b/nvbench/detail/stdrel_criterion.cxx
@@ -22,26 +22,17 @@ namespace nvbench::detail
 {
 
 stdrel_criterion::stdrel_criterion()
-    : stopping_criterion{"stdrel"}
+    : stopping_criterion{"stdrel",
+                         {{"max-noise", nvbench::detail::compat_max_noise()},
+                          {"min-time", nvbench::detail::compat_min_time()}}}
 {}
 
-void stdrel_criterion::initialize(const criterion_params &params)
+void stdrel_criterion::do_initialize()
 {
-  m_params = params;
   m_total_samples = 0;
   m_total_cuda_time = 0.0;
   m_cuda_times.clear();
   m_noise_tracker.clear();
-
-  if (m_params.has_value("max-noise"))
-  {
-    m_max_noise = m_params.get_float64("max-noise");
-  }
-
-  if (m_params.has_value("min-time"))
-  {
-    m_min_time = m_params.get_float64("min-time");
-  }
 }
 
 void stdrel_criterion::add_measurement(nvbench::float64_t measurement)
@@ -64,13 +55,13 @@ void stdrel_criterion::add_measurement(nvbench::float64_t measurement)
 
 bool stdrel_criterion::is_finished()
 {
-  if (m_total_cuda_time <= m_min_time) 
+  if (m_total_cuda_time <= m_params.get_float64("min-time"))
   {
     return false;
   }
 
   // Noise has dropped below threshold
-  if (m_noise_tracker.back() < m_max_noise)
+  if (m_noise_tracker.back() < m_params.get_float64("max-noise"))
   {
     return true;
   }
@@ -104,13 +95,4 @@ bool stdrel_criterion::is_finished()
   return false;
 }
 
-const stdrel_criterion::params_description &stdrel_criterion::get_params_description() const
-{
-  static const params_description desc{
-    {"max-noise", nvbench::named_values::type::float64},
-    {"min-time", nvbench::named_values::type::float64},
-  };
-  return desc;
-}
-
 } // namespace nvbench::detail
diff --git a/nvbench/option_parser.cu b/nvbench/option_parser.cu
index 4380ccd..26f8e1f 100644
--- a/nvbench/option_parser.cu
+++ b/nvbench/option_parser.cu
@@ -377,7 +377,7 @@ void option_parser::parse_range(option_parser::arg_iterator_t first,
     }
   };
 
-  const nvbench::stopping_criterion::params_description criterion_params =
+  const nvbench::criterion_manager::params_description criterion_params =
     nvbench::criterion_manager::get().get_params_description();
 
   while (first < last)
diff --git a/nvbench/state.cuh b/nvbench/state.cuh
index afd6291..09795de 100644
--- a/nvbench/state.cuh
+++ b/nvbench/state.cuh
@@ -149,16 +149,28 @@ struct state
 
   /// Accumulate at least this many seconds of timing data per measurement. 
   /// Only applies to `stdrel` stopping criterion. @{
-  [[nodiscard]] nvbench::float64_t get_min_time() const { return m_criterion_params.get_float64("min-time"); }
-  void set_min_time(nvbench::float64_t min_time) { m_criterion_params.set_float64("min-time", min_time); }
+  [[nodiscard]] nvbench::float64_t get_min_time() const
+  {
+    return m_criterion_params.get_float64("min-time");
+  }
+  void set_min_time(nvbench::float64_t min_time)
+  {
+    m_criterion_params.set_float64("min-time", min_time);
+  }
   /// @}
 
   /// Specify the maximum amount of noise if a measurement supports noise.
   /// Noise is the relative standard deviation:
-  /// `noise = stdev / mean_time`. 
+  /// `noise = stdev / mean_time`.
   /// Only applies to `stdrel` stopping criterion. @{
-  [[nodiscard]] nvbench::float64_t get_max_noise() const { return m_criterion_params.get_float64("max-noise"); }
-  void set_max_noise(nvbench::float64_t max_noise) { m_criterion_params.set_float64("max-noise", max_noise); }
+  [[nodiscard]] nvbench::float64_t get_max_noise() const
+  {
+    return m_criterion_params.get_float64("max-noise");
+  }
+  void set_max_noise(nvbench::float64_t max_noise)
+  {
+    m_criterion_params.set_float64("max-noise", max_noise);
+  }
   /// @}
 
   /// If a warmup run finishes in less than `skip_time`, the measurement will
diff --git a/nvbench/stopping_criterion.cuh b/nvbench/stopping_criterion.cuh
index 3abf9be..6a6b523 100644
--- a/nvbench/stopping_criterion.cuh
+++ b/nvbench/stopping_criterion.cuh
@@ -18,12 +18,14 @@
 
 #pragma once
 
-#include <nvbench/types.cuh>
 #include <nvbench/named_values.cuh>
+#include <nvbench/types.cuh>
 
-#include <unordered_map>
 #include <string>
 
+#include <initializer_list>
+#include <unordered_map>
+
 namespace nvbench
 {
 
@@ -42,14 +44,27 @@ class criterion_params
 {
   nvbench::named_values m_named_values;
 public:
+  criterion_params();
+  criterion_params(std::initializer_list<std::pair<std::string, nvbench::named_values::value_type>>);
+
+  /**
+   * Set parameter values from another criterion_params object if they exist
+   *
+   * Parameters in `other` that do not correspond to parameters in `this` are ignored.
+   */
+  void set_from(const criterion_params &other);
 
   void set_int64(std::string name, nvbench::int64_t value);
   void set_float64(std::string name, nvbench::float64_t value);
   void set_string(std::string name, std::string value);
 
+  [[nodiscard]] std::vector<std::string> get_names() const;
+  [[nodiscard]] nvbench::named_values::type get_type(const std::string &name) const;
+
   [[nodiscard]] bool has_value(const std::string &name) const;
   [[nodiscard]] nvbench::int64_t get_int64(const std::string &name) const;
   [[nodiscard]] nvbench::float64_t get_float64(const std::string &name) const;
+  [[nodiscard]] std::string get_string(const std::string &name) const;
 };
 
 /**
@@ -62,16 +77,28 @@ protected:
   criterion_params m_params;
 
 public:
-  explicit stopping_criterion(std::string name) : m_name(std::move(name)) { }
+  /**
+   * @param name Unique name of the criterion
+   * @param params Default values for all parameters of the criterion
+   */
+  explicit stopping_criterion(std::string name, criterion_params params)
+      : m_name{std::move(name)}
+      , m_params{params}
+  {}
 
   [[nodiscard]] const std::string &get_name() const { return m_name; }
+  [[nodiscard]] const criterion_params &get_params() const { return m_params; }
 
   /**
    * Initialize the criterion with the given parameters
    *
    * This method is called once per benchmark run, before any measurements are provided.
    */
-  virtual void initialize(const criterion_params &params) = 0;
+  void initialize(const criterion_params &params) 
+  {
+    m_params.set_from(params);
+    do_initialize();
+  }
 
   /**
    * Add the latest measurement to the criterion
@@ -83,12 +110,11 @@ public:
    */
   virtual bool is_finished() = 0;
 
-  using params_description = std::vector<std::pair<std::string, nvbench::named_values::type>>;
-
+protected:
   /**
-   * Return the parameter names and types for this criterion
+   * Initialize the criterion after updaring the parameters
    */
-  virtual const params_description &get_params_description() const = 0;
+  virtual void do_initialize() = 0;
 };
 
 } // namespace nvbench
diff --git a/nvbench/stopping_criterion.cxx b/nvbench/stopping_criterion.cxx
index 0659c7e..976a1a7 100644
--- a/nvbench/stopping_criterion.cxx
+++ b/nvbench/stopping_criterion.cxx
@@ -18,10 +18,48 @@
 
 #include <nvbench/stopping_criterion.cuh>
 
+#include <nvbench/detail/throw.cuh>
+
 
 namespace nvbench
 {
 
+// Default constructor for compatibility with old code
+criterion_params::criterion_params()
+    : criterion_params{{"max-noise", nvbench::detail::compat_max_noise()},
+                       {"min-time", nvbench::detail::compat_min_time()}}
+{}
+
+criterion_params::criterion_params(
+  std::initializer_list<std::pair<std::string, nvbench::named_values::value_type>> list)
+{
+  for (const auto &[name, value] : list)
+  {
+    m_named_values.set_value(name, value);
+  }
+}
+
+void criterion_params::set_from(const criterion_params &other)
+{
+  for (const std::string &name : this->get_names())
+  {
+    if (other.has_value(name))
+    {
+      if (this->get_type(name) != other.get_type(name))
+      {
+        NVBENCH_THROW(std::runtime_error,
+                      "Mismatched types for named value \"{}\". "
+                      "Expected {}, got {}.",
+                      name,
+                      static_cast<int>(this->get_type(name)),
+                      static_cast<int>(other.get_type(name)));
+      }
+      m_named_values.remove_value(name);
+      m_named_values.set_value(name, other.m_named_values.get_value(name));
+    }
+  }
+}
+
 void criterion_params::set_int64(std::string name, nvbench::int64_t value)
 {
   if (m_named_values.has_value(name)) 
@@ -54,10 +92,6 @@ void criterion_params::set_string(std::string name, std::string value)
 
 bool criterion_params::has_value(const std::string &name) const
 {
-  if (name == "max-noise" || name == "min-time")
-  { // compat
-    return true;
-  }
   return m_named_values.has_value(name);
 }
 
@@ -68,18 +102,23 @@ nvbench::int64_t criterion_params::get_int64(const std::string &name) const
 
 nvbench::float64_t criterion_params::get_float64(const std::string &name) const
 {
-  if (!m_named_values.has_value(name)) 
-  {
-    if (name == "max-noise")
-    { // compat
-      return nvbench::detail::compat_max_noise();
-    }
-    else if (name == "min-time")
-    { // compat
-      return nvbench::detail::compat_min_time();
-    }
-  }
   return m_named_values.get_float64(name);
 }
 
+std::string criterion_params::get_string(const std::string &name) const
+{
+  return m_named_values.get_string(name);
+}
+
+std::vector<std::string> criterion_params::get_names() const
+{
+  return m_named_values.get_names();
+}
+
+nvbench::named_values::type criterion_params::get_type(const std::string &name) const
+{
+  return m_named_values.get_type(name);
+}
+
+
 } // namespace nvbench::detail
diff --git a/testing/criterion_manager.cu b/testing/criterion_manager.cu
index 6c21eb1..f17f2c0 100644
--- a/testing/criterion_manager.cu
+++ b/testing/criterion_manager.cu
@@ -30,16 +30,15 @@ void test_standard_criteria_exist()
 class custom_criterion : public nvbench::stopping_criterion
 {
 public:
-  custom_criterion() : nvbench::stopping_criterion("custom") {}
+  custom_criterion()
+      : nvbench::stopping_criterion("custom", nvbench::criterion_params{})
+  {}
 
-  virtual void initialize(const nvbench::criterion_params &) override {}
   virtual void add_measurement(nvbench::float64_t /* measurement */) override {}
   virtual bool is_finished() override { return true; }
-  virtual const params_description &get_params_description() const override
-  {
-    static const params_description desc{};
-    return desc;
-  }
+
+protected:
+  virtual void do_initialize() override {}
 };
 
 void test_no_duplicates_are_allowed()