diff --git a/include/pybind11/detail/common.h b/include/pybind11/detail/common.h
index c7b69f58b..7397e2be9 100644
--- a/include/pybind11/detail/common.h
+++ b/include/pybind11/detail/common.h
@@ -689,6 +689,31 @@ template <typename T>
 struct is_input_iterator<T, void_t<decltype(*std::declval<T &>()), decltype(++std::declval<T &>())>>
     : std::true_type {};
 
+template <typename T> using is_function_pointer = bool_constant<
+    std::is_pointer<T>::value && std::is_function<typename std::remove_pointer<T>::type>::value>;
+
+template <typename F> struct strip_function_object {
+    using type = typename remove_class<decltype(&F::operator())>::type;
+};
+
+// Extracts the function signature from a function, function pointer or lambda.
+template <typename Function, typename F = remove_reference_t<Function>>
+using function_signature_t = conditional_t<
+    std::is_function<F>::value,
+    F,
+    typename conditional_t<
+        std::is_pointer<F>::value || std::is_member_pointer<F>::value,
+        std::remove_pointer<F>,
+        strip_function_object<F>
+    >::type
+>;
+
+/// Returns true if the type looks like a lambda: that is, isn't a function, pointer or member
+/// pointer.  Note that this can catch all sorts of other things, too; this is intended to be used
+/// in a place where passing a lambda makes sense.
+template <typename T> using is_lambda = satisfies_none_of<remove_reference_t<T>,
+        std::is_function, std::is_pointer, std::is_member_pointer>;
+
 /// Ignore that a variable is unused in compiler warnings
 inline void ignore_unused(const int *) { }
 
diff --git a/include/pybind11/numpy.h b/include/pybind11/numpy.h
index 4ee256192..4bea46029 100644
--- a/include/pybind11/numpy.h
+++ b/include/pybind11/numpy.h
@@ -1571,10 +1571,10 @@ vectorize(Return (*f) (Args ...)) {
 }
 
 // lambda vectorizer:
-template <typename Func, typename FuncType = typename detail::remove_class<decltype(&detail::remove_reference_t<Func>::operator())>::type>
+template <typename Func, detail::enable_if_t<detail::is_lambda<Func>::value, int> = 0>
 auto vectorize(Func &&f) -> decltype(
-        detail::vectorize_extractor(std::forward<Func>(f), (FuncType *) nullptr)) {
-    return detail::vectorize_extractor(std::forward<Func>(f), (FuncType *) nullptr);
+        detail::vectorize_extractor(std::forward<Func>(f), (detail::function_signature_t<Func> *) nullptr)) {
+    return detail::vectorize_extractor(std::forward<Func>(f), (detail::function_signature_t<Func> *) nullptr);
 }
 
 // Vectorize a class method (non-const):
diff --git a/include/pybind11/pybind11.h b/include/pybind11/pybind11.h
index 9bf39d145..bd0ee2733 100644
--- a/include/pybind11/pybind11.h
+++ b/include/pybind11/pybind11.h
@@ -58,16 +58,11 @@ public:
     }
 
     /// Construct a cpp_function from a lambda function (possibly with internal state)
-    template <typename Func, typename... Extra, typename = detail::enable_if_t<
-        detail::satisfies_none_of<
-            detail::remove_reference_t<Func>,
-            std::is_function, std::is_pointer, std::is_member_pointer
-        >::value>
-    >
+    template <typename Func, typename... Extra,
+              typename = detail::enable_if_t<detail::is_lambda<Func>::value>>
     cpp_function(Func &&f, const Extra&... extra) {
-        using FuncType = typename detail::remove_class<decltype(&detail::remove_reference_t<Func>::operator())>::type;
         initialize(std::forward<Func>(f),
-                   (FuncType *) nullptr, extra...);
+                   (detail::function_signature_t<Func> *) nullptr, extra...);
     }
 
     /// Construct a cpp_function from a class method (non-const)