diff --git a/include/pybind11/common.h b/include/pybind11/common.h
index fb8504cc..a1ee28ca 100644
--- a/include/pybind11/common.h
+++ b/include/pybind11/common.h
@@ -202,17 +202,6 @@ extern "C" {
     }                                                                          \
     PyObject *pybind11_init()
 
-// Function return value and argument type deduction support.  When compiling under C++17 these
-// differ as C++17 makes the noexcept specifier part of the function type, while it is not part of
-// the type under earlier standards.
-#ifdef __cpp_noexcept_function_type
-#  define PYBIND11_NOEXCEPT_TPL_ARG , bool NoExceptions
-#  define PYBIND11_NOEXCEPT_SPECIFIER noexcept(NoExceptions)
-#else
-#  define PYBIND11_NOEXCEPT_TPL_ARG
-#  define PYBIND11_NOEXCEPT_SPECIFIER
-#endif
-
 NAMESPACE_BEGIN(pybind11)
 
 using ssize_t = Py_ssize_t;
@@ -643,16 +632,16 @@ struct nodelete { template <typename T> void operator()(T*) { } };
 NAMESPACE_BEGIN(detail)
 template <typename... Args>
 struct overload_cast_impl {
-    template <typename Return /*,*/ PYBIND11_NOEXCEPT_TPL_ARG>
-    constexpr auto operator()(Return (*pf)(Args...) PYBIND11_NOEXCEPT_SPECIFIER) const noexcept
+    template <typename Return>
+    constexpr auto operator()(Return (*pf)(Args...)) const noexcept
                               -> decltype(pf) { return pf; }
 
-    template <typename Return, typename Class /*,*/ PYBIND11_NOEXCEPT_TPL_ARG>
-    constexpr auto operator()(Return (Class::*pmf)(Args...) PYBIND11_NOEXCEPT_SPECIFIER, std::false_type = {}) const noexcept
+    template <typename Return, typename Class>
+    constexpr auto operator()(Return (Class::*pmf)(Args...), std::false_type = {}) const noexcept
                               -> decltype(pmf) { return pmf; }
 
-    template <typename Return, typename Class /*,*/ PYBIND11_NOEXCEPT_TPL_ARG>
-    constexpr auto operator()(Return (Class::*pmf)(Args...) const PYBIND11_NOEXCEPT_SPECIFIER, std::true_type) const noexcept
+    template <typename Return, typename Class>
+    constexpr auto operator()(Return (Class::*pmf)(Args...) const, std::true_type) const noexcept
                               -> decltype(pmf) { return pmf; }
 };
 NAMESPACE_END(detail)
diff --git a/include/pybind11/functional.h b/include/pybind11/functional.h
index 8e7e75e6..b5ed4350 100644
--- a/include/pybind11/functional.h
+++ b/include/pybind11/functional.h
@@ -15,11 +15,11 @@
 NAMESPACE_BEGIN(pybind11)
 NAMESPACE_BEGIN(detail)
 
-template <typename Return, typename... Args /*,*/ PYBIND11_NOEXCEPT_TPL_ARG>
-struct type_caster<std::function<Return(Args...) PYBIND11_NOEXCEPT_SPECIFIER>> {
-    using type = std::function<Return(Args...) PYBIND11_NOEXCEPT_SPECIFIER>;
+template <typename Return, typename... Args>
+struct type_caster<std::function<Return(Args...)>> {
+    using type = std::function<Return(Args...)>;
     using retval_type = conditional_t<std::is_same<Return, void>::value, void_type, Return>;
-    using function_type = Return (*) (Args...) PYBIND11_NOEXCEPT_SPECIFIER;
+    using function_type = Return (*) (Args...);
 
 public:
     bool load(handle src_, bool) {
diff --git a/include/pybind11/numpy.h b/include/pybind11/numpy.h
index 50eb682d..5d78c3a6 100644
--- a/include/pybind11/numpy.h
+++ b/include/pybind11/numpy.h
@@ -1140,23 +1140,22 @@ template <typename T, int Flags> struct handle_type_name<array_t<T, Flags>> {
 
 NAMESPACE_END(detail)
 
-template <typename Func, typename Return, typename... Args /*,*/ PYBIND11_NOEXCEPT_TPL_ARG>
+template <typename Func, typename Return, typename... Args>
 detail::vectorize_helper<Func, Return, Args...>
-vectorize(const Func &f, Return (*) (Args ...) PYBIND11_NOEXCEPT_SPECIFIER) {
+vectorize(const Func &f, Return (*) (Args ...)) {
     return detail::vectorize_helper<Func, Return, Args...>(f);
 }
 
-template <typename Return, typename... Args /*,*/ PYBIND11_NOEXCEPT_TPL_ARG>
-detail::vectorize_helper<Return (*) (Args ...) PYBIND11_NOEXCEPT_SPECIFIER, Return, Args...>
-vectorize(Return (*f) (Args ...) PYBIND11_NOEXCEPT_SPECIFIER) {
+template <typename Return, typename... Args>
+detail::vectorize_helper<Return (*) (Args ...), Return, Args...>
+vectorize(Return (*f) (Args ...)) {
     return vectorize<Return (*) (Args ...), Return, Args...>(f, f);
 }
 
-template <typename Func>
+template <typename Func, typename FuncType = typename detail::remove_class<decltype(&std::remove_reference<Func>::type::operator())>::type>
 auto vectorize(Func &&f) -> decltype(
-        vectorize(std::forward<Func>(f), (typename detail::remove_class<decltype(&std::remove_reference<Func>::type::operator())>::type *) nullptr)) {
-    return vectorize(std::forward<Func>(f), (typename detail::remove_class<decltype(
-                   &std::remove_reference<Func>::type::operator())>::type *) nullptr);
+        vectorize(std::forward<Func>(f), (FuncType *) nullptr)) {
+    return vectorize(std::forward<Func>(f), (FuncType *) nullptr);
 }
 
 NAMESPACE_END(pybind11)
diff --git a/include/pybind11/pybind11.h b/include/pybind11/pybind11.h
index f022c0b4..5a604cd2 100644
--- a/include/pybind11/pybind11.h
+++ b/include/pybind11/pybind11.h
@@ -44,30 +44,31 @@ public:
     cpp_function() { }
 
     /// Construct a cpp_function from a vanilla function pointer
-    template <typename Return, typename... Args, typename... Extra /*,*/ PYBIND11_NOEXCEPT_TPL_ARG>
-    cpp_function(Return (*f)(Args...) PYBIND11_NOEXCEPT_SPECIFIER, const Extra&... extra) {
+    template <typename Return, typename... Args, typename... Extra>
+    cpp_function(Return (*f)(Args...), const Extra&... extra) {
         initialize(f, f, extra...);
     }
 
     /// Construct a cpp_function from a lambda function (possibly with internal state)
-    template <typename Func, typename... Extra> cpp_function(Func &&f, const Extra&... extra) {
+    template <typename Func, typename... Extra,
+             typename FuncType = typename detail::remove_class<decltype(&std::remove_reference<Func>::type::operator())>::type>
+    cpp_function(Func &&f, const Extra&... extra) {
         initialize(std::forward<Func>(f),
-                   (typename detail::remove_class<decltype(
-                       &std::remove_reference<Func>::type::operator())>::type *) nullptr, extra...);
+                   (FuncType *) nullptr, extra...);
     }
 
     /// Construct a cpp_function from a class method (non-const)
-    template <typename Return, typename Class, typename... Arg, typename... Extra /*,*/ PYBIND11_NOEXCEPT_TPL_ARG>
-    cpp_function(Return (Class::*f)(Arg...) PYBIND11_NOEXCEPT_SPECIFIER, const Extra&... extra) {
+    template <typename Return, typename Class, typename... Arg, typename... Extra>
+    cpp_function(Return (Class::*f)(Arg...), const Extra&... extra) {
         initialize([f](Class *c, Arg... args) -> Return { return (c->*f)(args...); },
-                   (Return (*) (Class *, Arg...) PYBIND11_NOEXCEPT_SPECIFIER) nullptr, extra...);
+                   (Return (*) (Class *, Arg...)) nullptr, extra...);
     }
 
     /// Construct a cpp_function from a class method (const)
-    template <typename Return, typename Class, typename... Arg, typename... Extra /*,*/ PYBIND11_NOEXCEPT_TPL_ARG>
-    cpp_function(Return (Class::*f)(Arg...) const PYBIND11_NOEXCEPT_SPECIFIER, const Extra&... extra) {
+    template <typename Return, typename Class, typename... Arg, typename... Extra>
+    cpp_function(Return (Class::*f)(Arg...) const, const Extra&... extra) {
         initialize([f](const Class *c, Arg... args) -> Return { return (c->*f)(args...); },
-                   (Return (*)(const Class *, Arg ...) PYBIND11_NOEXCEPT_SPECIFIER) nullptr, extra...);
+                   (Return (*)(const Class *, Arg ...)) nullptr, extra...);
     }
 
     /// Return the function name
@@ -80,8 +81,8 @@ protected:
     }
 
     /// Special internal constructor for functors, lambda functions, etc.
-    template <typename Func, typename Return, typename... Args, typename... Extra /*,*/ PYBIND11_NOEXCEPT_TPL_ARG>
-    void initialize(Func &&f, Return (*)(Args...) PYBIND11_NOEXCEPT_SPECIFIER, const Extra&... extra) {
+    template <typename Func, typename Return, typename... Args, typename... Extra>
+    void initialize(Func &&f, Return (*)(Args...), const Extra&... extra) {
 
         struct capture { typename std::remove_reference<Func>::type f; };
 
@@ -162,7 +163,7 @@ protected:
         if (cast_in::has_kwargs) rec->has_kwargs = true;
 
         /* Stash some additional information used by an important optimization in 'functional.h' */
-        using FunctionType = Return (*)(Args...) PYBIND11_NOEXCEPT_SPECIFIER;
+        using FunctionType = Return (*)(Args...);
         constexpr bool is_function_ptr =
             std::is_convertible<Func, FunctionType>::value &&
             sizeof(capture) == sizeof(void *);