diff --git a/include/pybind11/common.h b/include/pybind11/common.h
index 1a5f7fa4e..ed1bb610b 100644
--- a/include/pybind11/common.h
+++ b/include/pybind11/common.h
@@ -620,6 +620,11 @@ using exactly_one_t = typename exactly_one<Predicate, Default, Ts...>::type;
 template <typename T, typename... /*Us*/> struct deferred_type { using type = T; };
 template <typename T, typename... Us> using deferred_t = typename deferred_type<T, Us...>::type;
 
+/// Like is_base_of, but requires a strict base (i.e. `is_strict_base_of<T, T>::value == false`,
+/// unlike `std::is_base_of`)
+template <typename Base, typename Derived> using is_strict_base_of = bool_constant<
+    std::is_base_of<Base, Derived>::value && !std::is_same<Base, Derived>::value>;
+
 template <template<typename...> class Base>
 struct is_template_base_of_impl {
     template <typename... Us> static std::true_type check(Base<Us...> *);
diff --git a/include/pybind11/pybind11.h b/include/pybind11/pybind11.h
index e92290367..6084d968d 100644
--- a/include/pybind11/pybind11.h
+++ b/include/pybind11/pybind11.h
@@ -910,11 +910,22 @@ inline void call_operator_delete(void *p) { ::operator delete(p); }
 
 NAMESPACE_END(detail)
 
+/// Given a pointer to a member function, cast it to its `Derived` version.
+/// Forward everything else unchanged.
+template <typename /*Derived*/, typename F>
+auto method_adaptor(F &&f) -> decltype(std::forward<F>(f)) { return std::forward<F>(f); }
+
+template <typename Derived, typename Return, typename Class, typename... Args>
+auto method_adaptor(Return (Class::*pmf)(Args...)) -> Return (Derived::*)(Args...) { return pmf; }
+
+template <typename Derived, typename Return, typename Class, typename... Args>
+auto method_adaptor(Return (Class::*pmf)(Args...) const) -> Return (Derived::*)(Args...) const { return pmf; }
+
 template <typename type_, typename... options>
 class class_ : public detail::generic_type {
     template <typename T> using is_holder = detail::is_holder_type<type_, T>;
-    template <typename T> using is_subtype = detail::bool_constant<std::is_base_of<type_, T>::value && !std::is_same<T, type_>::value>;
-    template <typename T> using is_base = detail::bool_constant<std::is_base_of<T, type_>::value && !std::is_same<T, type_>::value>;
+    template <typename T> using is_subtype = detail::is_strict_base_of<type_, T>;
+    template <typename T> using is_base = detail::is_strict_base_of<T, type_>;
     // struct instead of using here to help MSVC:
     template <typename T> struct is_valid_class_option :
         detail::any_of<is_holder<T>, is_subtype<T>, is_base<T>> {};
@@ -980,7 +991,7 @@ public:
 
     template <typename Func, typename... Extra>
     class_ &def(const char *name_, Func&& f, const Extra&... extra) {
-        cpp_function cf(std::forward<Func>(f), name(name_), is_method(*this),
+        cpp_function cf(method_adaptor<type>(std::forward<Func>(f)), name(name_), is_method(*this),
                         sibling(getattr(*this, name_, none())), extra...);
         attr(cf.name()) = cf;
         return *this;
@@ -1044,15 +1055,17 @@ public:
 
     template <typename C, typename D, typename... Extra>
     class_ &def_readwrite(const char *name, D C::*pm, const Extra&... extra) {
-        cpp_function fget([pm](const C &c) -> const D &{ return c.*pm; }, is_method(*this)),
-                     fset([pm](C &c, const D &value) { c.*pm = value; }, is_method(*this));
+        static_assert(std::is_base_of<C, type>::value, "def_readwrite() requires a class member (or base class member)");
+        cpp_function fget([pm](const type &c) -> const D &{ return c.*pm; }, is_method(*this)),
+                     fset([pm](type &c, const D &value) { c.*pm = value; }, is_method(*this));
         def_property(name, fget, fset, return_value_policy::reference_internal, extra...);
         return *this;
     }
 
     template <typename C, typename D, typename... Extra>
     class_ &def_readonly(const char *name, const D C::*pm, const Extra& ...extra) {
-        cpp_function fget([pm](const C &c) -> const D &{ return c.*pm; }, is_method(*this));
+        static_assert(std::is_base_of<C, type>::value, "def_readonly() requires a class member (or base class member)");
+        cpp_function fget([pm](const type &c) -> const D &{ return c.*pm; }, is_method(*this));
         def_property_readonly(name, fget, return_value_policy::reference_internal, extra...);
         return *this;
     }
@@ -1075,7 +1088,8 @@ public:
     /// Uses return_value_policy::reference_internal by default
     template <typename Getter, typename... Extra>
     class_ &def_property_readonly(const char *name, const Getter &fget, const Extra& ...extra) {
-        return def_property_readonly(name, cpp_function(fget), return_value_policy::reference_internal, extra...);
+        return def_property_readonly(name, cpp_function(method_adaptor<type>(fget)),
+                                     return_value_policy::reference_internal, extra...);
     }
 
     /// Uses cpp_function's return_value_policy by default
@@ -1097,9 +1111,14 @@ public:
     }
 
     /// Uses return_value_policy::reference_internal by default
+    template <typename Getter, typename Setter, typename... Extra>
+    class_ &def_property(const char *name, const Getter &fget, const Setter &fset, const Extra& ...extra) {
+        return def_property(name, fget, cpp_function(method_adaptor<type>(fset)), extra...);
+    }
     template <typename Getter, typename... Extra>
     class_ &def_property(const char *name, const Getter &fget, const cpp_function &fset, const Extra& ...extra) {
-        return def_property(name, cpp_function(fget), fset, return_value_policy::reference_internal, extra...);
+        return def_property(name, cpp_function(method_adaptor<type>(fget)), fset,
+                            return_value_policy::reference_internal, extra...);
     }
 
     /// Uses cpp_function's return_value_policy by default
diff --git a/tests/test_methods_and_attributes.cpp b/tests/test_methods_and_attributes.cpp
index 670f6c3b7..e8e1b5224 100644
--- a/tests/test_methods_and_attributes.cpp
+++ b/tests/test_methods_and_attributes.cpp
@@ -159,7 +159,7 @@ public:
 };
 }}
 
-/// Issue/PR #648: bad arg default debugging output
+// Issue/PR #648: bad arg default debugging output
 class NotRegistered {};
 
 // Test None-allowed py::arg argument policy
@@ -177,6 +177,23 @@ struct StrIssue {
     StrIssue(int i) : val{i} {}
 };
 
+// Issues #854, #910: incompatible function args when member function/pointer is in unregistered base class
+class UnregisteredBase {
+public:
+    void do_nothing() const {}
+    void increase_value() { rw_value++; ro_value += 0.25; }
+    void set_int(int v) { rw_value = v; }
+    int get_int() const { return rw_value; }
+    double get_double() const { return ro_value; }
+    int rw_value = 42;
+    double ro_value = 1.25;
+};
+class RegisteredDerived : public UnregisteredBase {
+public:
+    using UnregisteredBase::UnregisteredBase;
+    double sum() const { return rw_value + ro_value; }
+};
+
 test_initializer methods_and_attributes([](py::module &m) {
     py::class_<ExampleMandA> emna(m, "ExampleMandA");
     emna.def(py::init<>())
@@ -325,7 +342,7 @@ test_initializer methods_and_attributes([](py::module &m) {
     m.def("ints_preferred", [](int i) { return i / 2; }, py::arg("i"));
     m.def("ints_only", [](int i) { return i / 2; }, py::arg("i").noconvert());
 
-    /// Issue/PR #648: bad arg default debugging output
+    // Issue/PR #648: bad arg default debugging output
 #if !defined(NDEBUG)
     m.attr("debug_enabled") = true;
 #else
@@ -360,4 +377,26 @@ test_initializer methods_and_attributes([](py::module &m) {
         .def("__str__", [](const StrIssue &si) {
             return "StrIssue[" + std::to_string(si.val) + "]"; }
         );
+
+    // Issues #854/910: incompatible function args when member function/pointer is in unregistered
+    // base class The methods and member pointers below actually resolve to members/pointers in
+    // UnregisteredBase; before this test/fix they would be registered via lambda with a first
+    // argument of an unregistered type, and thus uncallable.
+    py::class_<RegisteredDerived>(m, "RegisteredDerived")
+        .def(py::init<>())
+        .def("do_nothing", &RegisteredDerived::do_nothing)
+        .def("increase_value", &RegisteredDerived::increase_value)
+        .def_readwrite("rw_value", &RegisteredDerived::rw_value)
+        .def_readonly("ro_value", &RegisteredDerived::ro_value)
+        // These should trigger a static_assert if uncommented
+        //.def_readwrite("fails", &SimpleValue::value) // should trigger a static_assert if uncommented
+        //.def_readonly("fails", &SimpleValue::value) // should trigger a static_assert if uncommented
+        .def_property("rw_value_prop", &RegisteredDerived::get_int, &RegisteredDerived::set_int)
+        .def_property_readonly("ro_value_prop", &RegisteredDerived::get_double)
+        // This one is in the registered class:
+        .def("sum", &RegisteredDerived::sum)
+        ;
+
+    using Adapted = decltype(py::method_adaptor<RegisteredDerived>(&RegisteredDerived::do_nothing));
+    static_assert(std::is_same<Adapted, void (RegisteredDerived::*)() const>::value, "");
 });
diff --git a/tests/test_methods_and_attributes.py b/tests/test_methods_and_attributes.py
index 95049cfd4..afe8d2868 100644
--- a/tests/test_methods_and_attributes.py
+++ b/tests/test_methods_and_attributes.py
@@ -457,3 +457,23 @@ def test_str_issue(msg):
 
         Invoked with: 'no', 'such', 'constructor'
     """
+
+
+def test_unregistered_base_implementations():
+    from pybind11_tests import RegisteredDerived
+
+    a = RegisteredDerived()
+    a.do_nothing()
+    assert a.rw_value == 42
+    assert a.ro_value == 1.25
+    a.rw_value += 5
+    assert a.sum() == 48.25
+    a.increase_value()
+    assert a.rw_value == 48
+    assert a.ro_value == 1.5
+    assert a.sum() == 49.5
+    assert a.rw_value_prop == 48
+    a.rw_value_prop += 1
+    assert a.rw_value_prop == 49
+    a.increase_value()
+    assert a.ro_value_prop == 1.75