diff --git a/examples/co2injection_flash_ecfv.cpp b/examples/co2injection_flash_ecfv.cpp
index ea7358d96..cce743128 100644
--- a/examples/co2injection_flash_ecfv.cpp
+++ b/examples/co2injection_flash_ecfv.cpp
@@ -75,21 +75,11 @@ struct Scalar<TypeTag, TTag::Co2InjectionFlashEcfvProblem>
 
 } // namespace Opm::Properties
 
-namespace Opm::Parameters {
-
-#if ! HAVE_QUAD
-template<class TypeTag>
-struct NewtonTolerance<TypeTag, Properties::TTag::Co2InjectionFlashEcfvProblem>
-{
-    using type = GetPropType<TypeTag, Properties::Scalar>;
-    static constexpr type value = 1e-5;
-};
-#endif
-
-} // namespace Opm::Parameters
-
 int main(int argc, char **argv)
 {
     using EcfvProblemTypeTag = Opm::Properties::TTag::Co2InjectionFlashEcfvProblem;
+#if ! HAVE_QUAD
+    Opm::Co2InjectionTolerance = 1e-5;
+#endif
     return Opm::start<EcfvProblemTypeTag>(argc, argv);
 }
diff --git a/examples/co2injection_flash_ni_ecfv.cpp b/examples/co2injection_flash_ni_ecfv.cpp
index b5419ee75..36f0a8921 100644
--- a/examples/co2injection_flash_ni_ecfv.cpp
+++ b/examples/co2injection_flash_ni_ecfv.cpp
@@ -77,21 +77,11 @@ struct Scalar<TypeTag, TTag::Co2InjectionFlashNiEcfvProblem>
 
 } // namespace Opm::Properties
 
-namespace Opm::Parameters {
-
-#if ! HAVE_QUAD
-template<class TypeTag>
-struct NewtonTolerance<TypeTag, Properties::TTag::Co2InjectionFlashNiEcfvProblem>
-{
-    using type = GetPropType<TypeTag, Properties::Scalar>;
-    static constexpr type value = 1e-5;
-};
-#endif
-
-} // namespace Opm::Parameters
-
 int main(int argc, char **argv)
 {
     using EcfvProblemTypeTag = Opm::Properties::TTag::Co2InjectionFlashNiEcfvProblem;
+#if ! HAVE_QUAD
+    Opm::Co2InjectionTolerance = 1e-5;
+#endif
     return Opm::start<EcfvProblemTypeTag>(argc, argv);
 }
diff --git a/examples/co2injection_flash_ni_vcfv.cpp b/examples/co2injection_flash_ni_vcfv.cpp
index 99ea4cfbf..f448a67fe 100644
--- a/examples/co2injection_flash_ni_vcfv.cpp
+++ b/examples/co2injection_flash_ni_vcfv.cpp
@@ -73,21 +73,11 @@ struct Scalar<TypeTag, TTag::Co2InjectionFlashNiVcfvProblem>
 
 } // namespace Opm::Properties
 
-namespace Opm::Parameters {
-
-#if ! HAVE_QUAD
-template<class TypeTag>
-struct NewtonTolerance<TypeTag, Properties::TTag::Co2InjectionFlashNiVcfvProblem>
-{
-    using type = GetPropType<TypeTag, Properties::Scalar>;
-    static constexpr type value = 1e-5;
-};
-#endif
-
-} // namespace Opm::Parameters
-
 int main(int argc, char **argv)
 {
     using VcfvProblemTypeTag = Opm::Properties::TTag::Co2InjectionFlashNiVcfvProblem;
+#if ! HAVE_QUAD
+    Opm::Co2InjectionTolerance = 1e-5;
+#endif
     return Opm::start<VcfvProblemTypeTag>(argc, argv);
 }
diff --git a/examples/co2injection_flash_vcfv.cpp b/examples/co2injection_flash_vcfv.cpp
index 3c66fa159..d4a100e34 100644
--- a/examples/co2injection_flash_vcfv.cpp
+++ b/examples/co2injection_flash_vcfv.cpp
@@ -69,21 +69,11 @@ struct Scalar<TypeTag, TTag::Co2InjectionFlashVcfvProblem>
 
 } // namespace Opm::Properties
 
-namespace Opm::Parameters {
-
-#if ! HAVE_QUAD
-template<class TypeTag>
-struct NewtonTolerance<TypeTag, Properties::TTag::Co2InjectionFlashVcfvProblem>
-{
-    using type = GetPropType<TypeTag, Properties::Scalar>;
-    static constexpr type value = 1e-5;
-};
-#endif
-
-} // namespace Opm::Parameters
-
 int main(int argc, char **argv)
 {
     using VcfvProblemTypeTag = Opm::Properties::TTag::Co2InjectionFlashVcfvProblem;
+#if ! HAVE_QUAD
+    Opm::Co2InjectionTolerance = 1e-5;
+#endif
     return Opm::start<VcfvProblemTypeTag>(argc, argv);
 }
diff --git a/examples/problems/co2injectionproblem.hh b/examples/problems/co2injectionproblem.hh
index e28414a05..aa174b44a 100644
--- a/examples/problems/co2injectionproblem.hh
+++ b/examples/problems/co2injectionproblem.hh
@@ -231,6 +231,9 @@ struct Temperature<TypeTag, Properties::TTag::Co2InjectionBaseProblem>
 } // namespace Opm::Parameters
 
 namespace Opm {
+
+double Co2InjectionTolerance = 1e-8;
+
 /*!
  * \ingroup TestProblems
  *
@@ -393,6 +396,8 @@ public:
         Parameters::SetDefault<Parameters::GridFile>("data/co2injection.dgf");
         Parameters::SetDefault<Parameters::EndTime<Scalar>>(1e4);
         Parameters::SetDefault<Parameters::InitialTimeStepSize<Scalar>>(250);
+
+        Parameters::SetDefault<Parameters::NewtonTolerance<Scalar>>(Scalar{Co2InjectionTolerance});
     }
 
     /*!
diff --git a/examples/problems/co2ptflashproblem.hh b/examples/problems/co2ptflashproblem.hh
index 6116cc038..0e0e23bdd 100644
--- a/examples/problems/co2ptflashproblem.hh
+++ b/examples/problems/co2ptflashproblem.hh
@@ -190,13 +190,6 @@ struct LinearSolverTolerance<TypeTag, Properties::TTag::CO2PTBaseProblem>
     static constexpr type value = 1e-3;
 };
 
-template <class TypeTag>
-struct NewtonTolerance<TypeTag, Properties::TTag::CO2PTBaseProblem>
-{
-    using type = GetPropType<TypeTag, Properties::Scalar>;
-    static constexpr type value = 1e-3;
-};
-
 template <class TypeTag>
 struct NewtonTargetIterations<TypeTag, Properties::TTag::CO2PTBaseProblem>
 {
@@ -380,6 +373,7 @@ public:
 
         Parameters::SetDefault<Parameters::EndTime<Scalar>>(60. * 60.);
         Parameters::SetDefault<Parameters::InitialTimeStepSize<Scalar>>(0.1 * 60. * 60.);
+        Parameters::SetDefault<Parameters::NewtonTolerance<Scalar>>(1e-3);
     }
 
     /*!
diff --git a/examples/problems/reservoirproblem.hh b/examples/problems/reservoirproblem.hh
index c79c87adf..da41b8611 100644
--- a/examples/problems/reservoirproblem.hh
+++ b/examples/problems/reservoirproblem.hh
@@ -148,14 +148,6 @@ struct MaxDepth<TypeTag, Properties::TTag::ReservoirBaseProblem>
     static constexpr type value = 2500;
 };
 
-// increase the tolerance for this problem to get larger time steps
-template<class TypeTag>
-struct NewtonTolerance<TypeTag, Properties::TTag::ReservoirBaseProblem>
-{
-    using type = GetPropType<TypeTag, Properties::Scalar>;
-    static constexpr type value = 1e-6;
-};
-
 template<class TypeTag>
 struct Temperature<TypeTag, Properties::TTag::ReservoirBaseProblem>
 {
@@ -431,6 +423,8 @@ public:
         Parameters::SetDefault<Parameters::EnableStorageCache>(true);
         Parameters::SetDefault<Parameters::GridFile>("data/reservoir.dgf");
         Parameters::SetDefault<Parameters::InitialTimeStepSize<Scalar>>(100e3);
+        // increase the tolerance for this problem to get larger time steps
+        Parameters::SetDefault<Parameters::NewtonTolerance<Scalar>>(1e-6);
     }
 
     /*!
diff --git a/opm/models/nonlinear/newtonmethod.hh b/opm/models/nonlinear/newtonmethod.hh
index 81b5e12b2..26101dd51 100644
--- a/opm/models/nonlinear/newtonmethod.hh
+++ b/opm/models/nonlinear/newtonmethod.hh
@@ -81,13 +81,6 @@ struct NewtonConvergenceWriter<TypeTag, TTag::NewtonMethod> { using type = NullC
 
 namespace Opm::Parameters {
 
-template<class TypeTag>
-struct NewtonTolerance<TypeTag, Properties::TTag::NewtonMethod>
-{
-    using type = GetPropType<TypeTag, Properties::Scalar>;
-    static constexpr type value = 1e-8;
-};
-
 // set the abortion tolerance to some very large value. if not
 // overwritten at run-time this basically disables abortions
 template<class TypeTag>
@@ -146,7 +139,7 @@ public:
     {
         lastError_ = 1e100;
         error_ = 1e100;
-        tolerance_ = Parameters::get<TypeTag, Parameters::NewtonTolerance>();
+        tolerance_ = Parameters::Get<Parameters::NewtonTolerance<Scalar>>();
 
         numIterations_ = 0;
     }
@@ -168,7 +161,7 @@ public:
             ("The 'optimum' number of Newton iterations per time step");
         Parameters::registerParam<TypeTag, Parameters::NewtonMaxIterations>
             ("The maximum number of Newton iterations per time step");
-        Parameters::registerParam<TypeTag, Parameters::NewtonTolerance>
+        Parameters::Register<Parameters::NewtonTolerance<Scalar>>
             ("The maximum raw error tolerated by the Newton"
              "method for considering a solution to be converged");
         Parameters::registerParam<TypeTag, Parameters::NewtonMaxError>
diff --git a/opm/models/nonlinear/newtonmethodparameters.hh b/opm/models/nonlinear/newtonmethodparameters.hh
index 80b1f098e..35c16379c 100644
--- a/opm/models/nonlinear/newtonmethodparameters.hh
+++ b/opm/models/nonlinear/newtonmethodparameters.hh
@@ -27,21 +27,21 @@
 
 namespace Opm::Parameters {
 
-//! Specifies whether the Newton method should print messages or not
-struct NewtonVerbose { static constexpr bool value = true; };
-
-//! Specifies whether the convergence rate and the global residual
-//! gets written out to disk for every Newton iteration
-struct NewtonWriteConvergence { static constexpr bool value = false; };
-
 /*!
  * \brief The value for the error below which convergence is declared
  *
  * This value can (and for the porous media models will) be changed to account for grid
  * scaling and other effects.
  */
-template<class TypeTag, class MyTypeTag>
-struct NewtonTolerance { using type = Properties::UndefinedProperty; };
+template<class Scalar>
+struct NewtonTolerance { static constexpr Scalar value = 1e-8; };
+
+//! Specifies whether the Newton method should print messages or not
+struct NewtonVerbose { static constexpr bool value = true; };
+
+//! Specifies whether the convergence rate and the global residual
+//! gets written out to disk for every Newton iteration
+struct NewtonWriteConvergence { static constexpr bool value = false; };
 
 //! The maximum error which may occur in a simulation before the
 //! Newton method for the time step is aborted