diff --git a/docs/advanced/classes.rst b/docs/advanced/classes.rst
index 9d17364..e0463b4 100644
--- a/docs/advanced/classes.rst
+++ b/docs/advanced/classes.rst
@@ -388,6 +388,8 @@
     py::class_<MyClass, std::unique_ptr<MyClass, py::nodelete>>(m, "MyClass")
         .def(py::init<>())
 
+.. _implicit_conversions:
+
 Implicit conversions
 ====================
 
diff --git a/docs/advanced/functions.rst b/docs/advanced/functions.rst
index 7ffdfaa..e67d7bc 100644
--- a/docs/advanced/functions.rst
+++ b/docs/advanced/functions.rst
@@ -318,3 +318,57 @@
 
     py::class_<MyClass>("MyClass")
         .def("myFunction", py::arg("arg") = (SomeType *) nullptr);
+
+Non-converting arguments
+========================
+
+Certain argument types may support conversion from one type to another.  Some
+examples of conversions are:
+
+* :ref:`implicit_conversions` declared using ``py::implicitly_convertible<A,B>()``
+* Calling a method accepting a double with an integer argument
+* Calling a ``std::complex<float>`` argument with a non-complex python type
+  (for example, with a float).  (Requires the optional ``pybind11/complex.h``
+  header).
+* Calling a function taking an Eigen matrix reference with a numpy array of the
+  wrong type or of an incompatible data layout.  (Requires the optional
+  ``pybind11/eigen.h`` header).
+
+This behaviour is sometimes undesirable: the binding code may prefer to raise
+an error rather than convert the argument.  This behaviour can be obtained
+through ``py::arg`` by calling the ``.noconvert()`` method of the ``py::arg``
+object, such as:
+
+.. code-block:: cpp
+
+    m.def("floats_only", [](double f) { return 0.5 * f; }, py::arg("f").noconvert());
+    m.def("floats_preferred", [](double f) { return 0.5 * f; }, py::arg("f"));
+
+Attempting the call the second function (the one without ``.noconvert()``) with
+an integer will succeed, but attempting to call the ``.noconvert()`` version
+will fail with a ``TypeError``:
+
+.. code-block:: pycon
+
+    >>> floats_preferred(4)
+    2.0
+    >>> floats_only(4)
+    Traceback (most recent call last):
+      File "<stdin>", line 1, in <module>
+    TypeError: floats_only(): incompatible function arguments. The following argument types are supported:
+        1. (f: float) -> float
+
+    Invoked with: 4
+
+You may, of course, combine this with the :var:`_a` shorthand notation (see
+:ref:`keyword_args`) and/or :ref:`default_args`.  It is also permitted to omit
+the argument name by using the ``py::arg()`` constructor without an argument
+name, i.e. by specifying ``py::arg().noconvert()``.
+
+.. note::
+
+    When specifying ``py::arg`` options it is necessary to provide the same
+    number of options as the bound function has arguments.  Thus if you want to
+    enable no-convert behaviour for just one of several arguments, you will
+    need to specify a ``py::arg()`` annotation for each argument with the
+    no-convert argument modified to ``py::arg().noconvert()``.
diff --git a/include/pybind11/attr.h b/include/pybind11/attr.h
index e9468b8..129db05 100644
--- a/include/pybind11/attr.h
+++ b/include/pybind11/attr.h
@@ -69,7 +69,6 @@
 template <op_id id, op_type ot, typename L = undefined_t, typename R = undefined_t> struct op_;
 template <typename... Args> struct init;
 template <typename... Args> struct init_alias;
-struct function_call;
 inline void keep_alive_impl(size_t Nurse, size_t Patient, function_call &call, handle ret);
 
 /// Internal data structure which holds metadata about a keyword argument
@@ -77,9 +76,10 @@
     const char *name;  ///< Argument name
     const char *descr; ///< Human-readable version of the argument value
     handle value;      ///< Associated Python object
+    bool convert : 1;  ///< True if the argument is allowed to convert when loading
 
-    argument_record(const char *name, const char *descr, handle value)
-        : name(name), descr(descr), value(value) { }
+    argument_record(const char *name, const char *descr, handle value, bool convert)
+        : name(name), descr(descr), value(value), convert(convert) { }
 };
 
 /// Internal data structure which holds metadata about a bound function (signature, overloads, etc.)
@@ -131,7 +131,7 @@
     bool is_method : 1;
 
     /// Number of arguments (including py::args and/or py::kwargs, if present)
-    uint16_t nargs;
+    std::uint16_t nargs;
 
     /// Python method object
     PyMethodDef *def = nullptr;
@@ -222,21 +222,11 @@
     }
 };
 
-/// Internal data associated with a single function call
-struct function_call {
-    function_call(function_record &f, handle p) : func(f), parent(p) {
-        args.reserve(f.nargs);
-    }
-
-    /// The function data:
-    const function_record &func;
-
-    /// Arguments passed to the function:
-    std::vector<handle> args;
-
-    /// The parent, if any
-    handle parent;
-};
+inline function_call::function_call(function_record &f, handle p) :
+        func(f), parent(p) {
+    args.reserve(f.nargs);
+    args_convert.reserve(f.nargs);
+}
 
 /**
  * Partial template specializations to process custom attributes provided to
@@ -300,8 +290,8 @@
 template <> struct process_attribute<arg> : process_attribute_default<arg> {
     static void init(const arg &a, function_record *r) {
         if (r->is_method && r->args.empty())
-            r->args.emplace_back("self", nullptr, handle());
-        r->args.emplace_back(a.name, nullptr, handle());
+            r->args.emplace_back("self", nullptr, handle(), true /*convert*/);
+        r->args.emplace_back(a.name, nullptr, handle(), !a.flag_noconvert);
     }
 };
 
@@ -309,7 +299,7 @@
 template <> struct process_attribute<arg_v> : process_attribute_default<arg_v> {
     static void init(const arg_v &a, function_record *r) {
         if (r->is_method && r->args.empty())
-            r->args.emplace_back("self", nullptr, handle());
+            r->args.emplace_back("self", nullptr /*descr*/, handle() /*parent*/, true /*convert*/);
 
         if (!a.value) {
 #if !defined(NDEBUG)
@@ -330,7 +320,7 @@
                           "Compile in debug mode for more information.");
 #endif
         }
-        r->args.emplace_back(a.name, a.descr, a.value.inc_ref());
+        r->args.emplace_back(a.name, a.descr, a.value.inc_ref(), !a.flag_noconvert);
     }
 };
 
diff --git a/include/pybind11/cast.h b/include/pybind11/cast.h
index 4dc3082..67ab216 100644
--- a/include/pybind11/cast.h
+++ b/include/pybind11/cast.h
@@ -1202,22 +1202,26 @@
 }
 
 /// \ingroup annotations
-/// Annotation for keyword arguments
+/// Annotation for arguments
 struct arg {
-    /// Set the name of the argument
-    constexpr explicit arg(const char *name) : name(name) { }
+    /// Constructs an argument with the name of the argument; if null or omitted, this is a positional argument.
+    constexpr explicit arg(const char *name = nullptr) : name(name), flag_noconvert(false) { }
     /// Assign a value to this argument
     template <typename T> arg_v operator=(T &&value) const;
+    /// Indicate that the type should not be converted in the type caster
+    arg &noconvert(bool flag = true) { flag_noconvert = flag; return *this; }
 
-    const char *name;
+    const char *name; ///< If non-null, this is a named kwargs argument
+    bool flag_noconvert : 1; ///< If set, do not allow conversion (requires a supporting type caster!)
 };
 
 /// \ingroup annotations
-/// Annotation for keyword arguments with values
+/// Annotation for arguments with values
 struct arg_v : arg {
+private:
     template <typename T>
-    arg_v(const char *name, T &&x, const char *descr = nullptr)
-        : arg(name),
+    arg_v(arg &&base, T &&x, const char *descr = nullptr)
+        : arg(base),
           value(reinterpret_steal<object>(
               detail::make_caster<T>::cast(x, return_value_policy::automatic, {})
           )),
@@ -1227,15 +1231,32 @@
 #endif
     { }
 
+public:
+    /// Direct construction with name, default, and description
+    template <typename T>
+    arg_v(const char *name, T &&x, const char *descr = nullptr)
+        : arg_v(arg(name), std::forward<T>(x), descr) { }
+
+    /// Called internally when invoking `py::arg("a") = value`
+    template <typename T>
+    arg_v(const arg &base, T &&x, const char *descr = nullptr)
+        : arg_v(arg(base), std::forward<T>(x), descr) { }
+
+    /// Same as `arg::noconvert()`, but returns *this as arg_v&, not arg&
+    arg_v &noconvert(bool flag = true) { arg::noconvert(flag); return *this; }
+
+    /// The default value
     object value;
+    /// The (optional) description of the default value
     const char *descr;
 #if !defined(NDEBUG)
+    /// The C++ type name of the default value (only available when compiled in debug mode)
     std::string type;
 #endif
 };
 
 template <typename T>
-arg_v arg::operator=(T &&value) const { return {name, std::forward<T>(value)}; }
+arg_v arg::operator=(T &&value) const { return {std::move(*this), std::forward<T>(value)}; }
 
 /// Alias for backward compatibility -- to be removed in version 2.0
 template <typename /*unused*/> using arg_t = arg_v;
@@ -1252,11 +1273,28 @@
 // forward declaration
 struct function_record;
 
+/// Internal data associated with a single function call
+struct function_call {
+    function_call(function_record &f, handle p); // Implementation in attr.h
+
+    /// The function data:
+    const function_record &func;
+
+    /// Arguments passed to the function:
+    std::vector<handle> args;
+
+    /// The `convert` value the arguments should be loaded with
+    std::vector<bool> args_convert;
+
+    /// The parent, if any
+    handle parent;
+};
+
+
 /// Helper class which loads arguments for C++ functions called from Python
 template <typename... Args>
 class argument_loader {
     using indices = make_index_sequence<sizeof...(Args)>;
-    using function_arguments = const std::vector<handle> &;
 
     template <typename Arg> using argument_is_args   = std::is_same<intrinsic_t<Arg>, args>;
     template <typename Arg> using argument_is_kwargs = std::is_same<intrinsic_t<Arg>, kwargs>;
@@ -1274,8 +1312,8 @@
 
     static PYBIND11_DESCR arg_names() { return detail::concat(make_caster<Args>::name()...); }
 
-    bool load_args(function_arguments args) {
-        return load_impl_sequence(args, indices{});
+    bool load_args(function_call &call) {
+        return load_impl_sequence(call, indices{});
     }
 
     template <typename Return, typename Func>
@@ -1291,11 +1329,11 @@
 
 private:
 
-    static bool load_impl_sequence(function_arguments, index_sequence<>) { return true; }
+    static bool load_impl_sequence(function_call &, index_sequence<>) { return true; }
 
     template <size_t... Is>
-    bool load_impl_sequence(function_arguments args, index_sequence<Is...>) {
-        for (bool r : {std::get<Is>(value).load(args[Is], true)...})
+    bool load_impl_sequence(function_call &call, index_sequence<Is...>) {
+        for (bool r : {std::get<Is>(value).load(call.args[Is], call.args_convert[Is])...})
             if (!r)
                 return false;
         return true;
@@ -1384,6 +1422,13 @@
     }
 
     void process(list &/*args_list*/, arg_v a) {
+        if (!a.name)
+#if defined(NDEBUG)
+            nameless_argument_error();
+#else
+            nameless_argument_error(a.type);
+#endif
+
         if (m_kwargs.contains(a.name)) {
 #if defined(NDEBUG)
             multiple_values_error();
@@ -1416,6 +1461,15 @@
         }
     }
 
+    [[noreturn]] static void nameless_argument_error() {
+        throw type_error("Got kwargs without a name; only named arguments "
+                         "may be passed via py::arg() to a python function call. "
+                         "(compile in debug mode for details)");
+    }
+    [[noreturn]] static void nameless_argument_error(std::string type) {
+        throw type_error("Got kwargs without a name of type '" + type + "'; only named "
+                         "arguments may be passed via py::arg() to a python function call. ");
+    }
     [[noreturn]] static void multiple_values_error() {
         throw type_error("Got multiple values for keyword argument "
                          "(compile in debug mode for details)");
diff --git a/include/pybind11/pybind11.h b/include/pybind11/pybind11.h
index 14dc56c..fc28370 100644
--- a/include/pybind11/pybind11.h
+++ b/include/pybind11/pybind11.h
@@ -122,7 +122,7 @@
             cast_in args_converter;
 
             /* Try to cast the function arguments into the C++ domain */
-            if (!args_converter.load_args(call.args))
+            if (!args_converter.load_args(call))
                 return PYBIND11_TRY_NEXT_OVERLOAD;
 
             /* Invoke call policy pre-call hook */
@@ -198,7 +198,7 @@
             if (c == '{') {
                 // Write arg name for everything except *args, **kwargs and return type.
                 if (type_depth == 0 && text[char_index] != '*' && arg_index < args) {
-                    if (!rec->args.empty()) {
+                    if (!rec->args.empty() && rec->args[arg_index].name) {
                         signature += rec->args[arg_index].name;
                     } else if (arg_index == 0 && rec->is_method) {
                         signature += "self";
@@ -257,7 +257,7 @@
         rec->signature = strdup(signature.c_str());
         rec->args.shrink_to_fit();
         rec->is_constructor = !strcmp(rec->name, "__init__") || !strcmp(rec->name, "__setstate__");
-        rec->nargs = (uint16_t) args;
+        rec->nargs = (std::uint16_t) args;
 
 #if PY_MAJOR_VERSION < 3
         if (rec->sibling && PyMethod_Check(rec->sibling.ptr()))
@@ -392,8 +392,10 @@
 
         handle parent = n_args_in > 0 ? PyTuple_GET_ITEM(args_in, 0) : nullptr,
                result = PYBIND11_TRY_NEXT_OVERLOAD;
+
         try {
             for (; it != nullptr; it = it->next) {
+
                 /* For each overload:
                    1. Copy all positional arguments we were given, also checking to make sure that
                       named positional arguments weren't *also* specified via kwarg.
@@ -435,14 +437,15 @@
                     // raise a TypeError like Python does.  (We could also continue with the next
                     // overload, but this seems highly likely to be a caller mistake rather than a
                     // legitimate overload).
-                    if (kwargs_in && args_copied < it->args.size()) {
-                        handle value = PyDict_GetItemString(kwargs_in, it->args[args_copied].name);
+                    if (kwargs_in && args_copied < func.args.size() && func.args[args_copied].name) {
+                        handle value = PyDict_GetItemString(kwargs_in, func.args[args_copied].name);
                         if (value)
-                            throw type_error(std::string(it->name) + "(): got multiple values for argument '" +
-                                    std::string(it->args[args_copied].name) + "'");
+                            throw type_error(std::string(func.name) + "(): got multiple values for argument '" +
+                                    std::string(func.args[args_copied].name) + "'");
                     }
 
                     call.args.push_back(PyTuple_GET_ITEM(args_in, args_copied));
+                    call.args_convert.push_back(args_copied < func.args.size() ? func.args[args_copied].convert : true);
                 }
 
                 // We'll need to copy this if we steal some kwargs for defaults
@@ -453,10 +456,10 @@
                     bool copied_kwargs = false;
 
                     for (; args_copied < pos_args; ++args_copied) {
-                        const auto &arg = it->args[args_copied];
+                        const auto &arg = func.args[args_copied];
 
                         handle value;
-                        if (kwargs_in)
+                        if (kwargs_in && arg.name)
                             value = PyDict_GetItemString(kwargs.ptr(), arg.name);
 
                         if (value) {
@@ -470,8 +473,10 @@
                             value = arg.value;
                         }
 
-                        if (value)
+                        if (value) {
                             call.args.push_back(value);
+                            call.args_convert.push_back(arg.convert);
+                        }
                         else
                             break;
                     }
@@ -481,12 +486,12 @@
                 }
 
                 // 3. Check everything was consumed (unless we have a kwargs arg)
-                if (kwargs && kwargs.size() > 0 && !it->has_kwargs)
+                if (kwargs && kwargs.size() > 0 && !func.has_kwargs)
                     continue; // Unconsumed kwargs, but no py::kwargs argument to accept them
 
                 // 4a. If we have a py::args argument, create a new tuple with leftovers
                 tuple extra_args;
-                if (it->has_args) {
+                if (func.has_args) {
                     if (args_to_copy == 0) {
                         // We didn't copy out any position arguments from the args_in tuple, so we
                         // can reuse it directly without copying:
@@ -502,31 +507,34 @@
                         }
                     }
                     call.args.push_back(extra_args);
+                    call.args_convert.push_back(false);
                 }
 
                 // 4b. If we have a py::kwargs, pass on any remaining kwargs
-                if (it->has_kwargs) {
+                if (func.has_kwargs) {
                     if (!kwargs.ptr())
                         kwargs = dict(); // If we didn't get one, send an empty one
                     call.args.push_back(kwargs);
+                    call.args_convert.push_back(false);
                 }
 
                 // 5. Put everything in a vector.  Not technically step 5, we've been building it
                 // in `call.args` all along.
                 #if !defined(NDEBUG)
-                if (call.args.size() != call.func.nargs)
+                if (call.args.size() != func.nargs || call.args_convert.size() != func.nargs)
                     pybind11_fail("Internal error: function call dispatcher inserted wrong number of arguments!");
                 #endif
 
                 // 6. Call the function.
                 try {
-                    result = it->impl(call);
+                    result = func.impl(call);
                 } catch (reference_cast_error &) {
                     result = PYBIND11_TRY_NEXT_OVERLOAD;
                 }
 
                 if (result.ptr() != PYBIND11_TRY_NEXT_OVERLOAD)
                     break;
+
             }
         } catch (error_already_set &e) {
             e.restore();
diff --git a/tests/test_methods_and_attributes.cpp b/tests/test_methods_and_attributes.cpp
index f7d6d68..6f5e5ef 100644
--- a/tests/test_methods_and_attributes.cpp
+++ b/tests/test_methods_and_attributes.cpp
@@ -97,6 +97,42 @@
 
 class CppDerivedDynamicClass : public DynamicClass { };
 
+// py::arg/py::arg_v testing: these arguments just record their argument when invoked
+class ArgInspector1 { public: std::string arg = "(default arg inspector 1)"; };
+class ArgInspector2 { public: std::string arg = "(default arg inspector 2)"; };
+namespace pybind11 { namespace detail {
+template <> struct type_caster<ArgInspector1> {
+public:
+    PYBIND11_TYPE_CASTER(ArgInspector1, _("ArgInspector1"));
+
+    bool load(handle src, bool convert) {
+        value.arg = "loading ArgInspector1 argument " +
+            std::string(convert ? "WITH" : "WITHOUT") + " conversion allowed.  "
+            "Argument value = " + (std::string) str(src);
+        return true;
+    }
+
+    static handle cast(const ArgInspector1 &src, return_value_policy, handle) {
+        return str(src.arg).release();
+    }
+};
+template <> struct type_caster<ArgInspector2> {
+public:
+    PYBIND11_TYPE_CASTER(ArgInspector2, _("ArgInspector2"));
+
+    bool load(handle src, bool convert) {
+        value.arg = "loading ArgInspector2 argument " +
+            std::string(convert ? "WITH" : "WITHOUT") + " conversion allowed.  "
+            "Argument value = " + (std::string) str(src);
+        return true;
+    }
+
+    static handle cast(const ArgInspector2 &src, return_value_policy, handle) {
+        return str(src.arg).release();
+    }
+};
+}}
+
 test_initializer methods_and_attributes([](py::module &m) {
     py::class_<ExampleMandA>(m, "ExampleMandA")
         .def(py::init<>())
@@ -183,4 +219,25 @@
     py::class_<CppDerivedDynamicClass, DynamicClass>(m, "CppDerivedDynamicClass")
         .def(py::init());
 #endif
+
+    class ArgInspector {
+    public:
+        ArgInspector1 f(ArgInspector1 a) { return a; }
+        std::string g(ArgInspector1 a, const ArgInspector1 &b, int c, ArgInspector2 *d) {
+            return a.arg + "\n" + b.arg + "\n" + std::to_string(c) + "\n" + d->arg;
+        }
+        static ArgInspector2 h(ArgInspector2 a) { return a; }
+    };
+    py::class_<ArgInspector>(m, "ArgInspector")
+        .def(py::init<>())
+        .def("f", &ArgInspector::f)
+        .def("g", &ArgInspector::g, "a"_a.noconvert(), "b"_a, "c"_a.noconvert()=13, "d"_a=ArgInspector2())
+        .def_static("h", &ArgInspector::h, py::arg().noconvert())
+        ;
+    m.def("arg_inspect_func", [](ArgInspector2 a, ArgInspector1 b) { return a.arg + "\n" + b.arg; },
+            py::arg().noconvert(false), py::arg_v(nullptr, ArgInspector1()).noconvert(true));
+
+    m.def("floats_preferred", [](double f) { return 0.5 * f; }, py::arg("f"));
+    m.def("floats_only", [](double f) { return 0.5 * f; }, py::arg("f").noconvert());
+
 });
diff --git a/tests/test_methods_and_attributes.py b/tests/test_methods_and_attributes.py
index 840ee70..f890c6a 100644
--- a/tests/test_methods_and_attributes.py
+++ b/tests/test_methods_and_attributes.py
@@ -203,3 +203,47 @@
     assert cstats.alive() == 2
     del i1, i2
     assert cstats.alive() == 0
+
+
+def test_noconvert_args(msg):
+    from pybind11_tests import ArgInspector, arg_inspect_func, floats_only, floats_preferred
+
+    a = ArgInspector()
+    assert msg(a.f("hi")) == """
+        loading ArgInspector1 argument WITH conversion allowed.  Argument value = hi
+    """
+    assert msg(a.g("this is a", "this is b")) == """
+        loading ArgInspector1 argument WITHOUT conversion allowed.  Argument value = this is a
+        loading ArgInspector1 argument WITH conversion allowed.  Argument value = this is b
+        13
+        loading ArgInspector2 argument WITH conversion allowed.  Argument value = (default arg inspector 2)
+    """  # noqa: E501 line too long
+    assert msg(a.g("this is a", "this is b", 42)) == """
+        loading ArgInspector1 argument WITHOUT conversion allowed.  Argument value = this is a
+        loading ArgInspector1 argument WITH conversion allowed.  Argument value = this is b
+        42
+        loading ArgInspector2 argument WITH conversion allowed.  Argument value = (default arg inspector 2)
+    """  # noqa: E501 line too long
+    assert msg(a.g("this is a", "this is b", 42, "this is d")) == """
+        loading ArgInspector1 argument WITHOUT conversion allowed.  Argument value = this is a
+        loading ArgInspector1 argument WITH conversion allowed.  Argument value = this is b
+        42
+        loading ArgInspector2 argument WITH conversion allowed.  Argument value = this is d
+    """
+    assert (a.h("arg 1") ==
+            "loading ArgInspector2 argument WITHOUT conversion allowed.  Argument value = arg 1")
+    assert msg(arg_inspect_func("A1", "A2")) == """
+        loading ArgInspector2 argument WITH conversion allowed.  Argument value = A1
+        loading ArgInspector1 argument WITHOUT conversion allowed.  Argument value = A2
+    """
+
+    assert floats_preferred(4) == 2.0
+    assert floats_only(4.0) == 2.0
+    with pytest.raises(TypeError) as excinfo:
+        floats_only(4)
+    assert msg(excinfo.value) == """
+        floats_only(): incompatible function arguments. The following argument types are supported:
+            1. (f: float) -> float
+
+        Invoked with: 4
+    """