diff --git a/tests/conftest.py b/tests/conftest.py
index d4335fc..b69fd6c 100644
--- a/tests/conftest.py
+++ b/tests/conftest.py
@@ -10,6 +10,8 @@
 import re
 import sys
 import contextlib
+import platform
+import gc
 
 _unicode_marker = re.compile(r'u(\'[^\']*\')')
 _long_marker = re.compile(r'([0-9])L')
@@ -176,6 +178,13 @@
         pass
 
 
+def gc_collect():
+    ''' Run the garbage collector twice (needed when running
+    reference counting tests with PyPy) '''
+    gc.collect()
+    gc.collect()
+
+
 def pytest_namespace():
     """Add import suppression and test requirements to `pytest` namespace"""
     try:
@@ -190,6 +199,7 @@
         from pybind11_tests import have_eigen
     except ImportError:
         have_eigen = False
+    pypy = platform.python_implementation() == "PyPy"
 
     skipif = pytest.mark.skipif
     return {
@@ -200,6 +210,8 @@
                                            reason="eigen and/or numpy are not installed"),
         'requires_eigen_and_scipy': skipif(not have_eigen or not scipy,
                                            reason="eigen and/or scipy are not installed"),
+        'unsupported_on_pypy': skipif(pypy, reason="unsupported on PyPy"),
+        'gc_collect': gc_collect
     }
 
 
diff --git a/tests/constructor_stats.h b/tests/constructor_stats.h
index eb3e49c..de5c133 100644
--- a/tests/constructor_stats.h
+++ b/tests/constructor_stats.h
@@ -85,27 +85,51 @@
         created(inst);
         copy_constructions++;
     }
+
     void move_created(void *inst) {
         created(inst);
         move_constructions++;
     }
+
     void default_created(void *inst) {
         created(inst);
         default_constructions++;
     }
+
     void created(void *inst) {
         ++_instances[inst];
-    };
+    }
+
     void destroyed(void *inst) {
         if (--_instances[inst] < 0)
-            throw std::runtime_error("cstats.destroyed() called with unknown instance; potential double-destruction or a missing cstats.created()");
+            throw std::runtime_error("cstats.destroyed() called with unknown "
+                                     "instance; potential double-destruction "
+                                     "or a missing cstats.created()");
+    }
+
+    static void gc() {
+        // Force garbage collection to ensure any pending destructors are invoked:
+#if defined(PYPY_VERSION)
+        PyObject *globals = PyEval_GetGlobals();
+        PyObject *result = PyRun_String(
+            "import gc\n"
+            "for i in range(2):"
+            "    gc.collect()\n",
+            Py_file_input, globals, globals);
+        if (result == nullptr)
+            throw py::error_already_set();
+        Py_DECREF(result);
+#else
+        py::module::import("gc").attr("collect")();
+#endif
     }
 
     int alive() {
-        // Force garbage collection to ensure any pending destructors are invoked:
-        py::module::import("gc").attr("collect")();
+        gc();
         int total = 0;
-        for (const auto &p : _instances) if (p.second > 0) total += p.second;
+        for (const auto &p : _instances)
+            if (p.second > 0)
+                total += p.second;
         return total;
     }
 
@@ -134,6 +158,9 @@
 
     // Gets constructor stats from a C++ type
     template <typename T> static ConstructorStats& get() {
+#if defined(PYPY_VERSION)
+        gc();
+#endif
         return get(typeid(T));
     }
 
diff --git a/tests/test_alias_initialization.py b/tests/test_alias_initialization.py
index 0ed9d2f..fb90cfc 100644
--- a/tests/test_alias_initialization.py
+++ b/tests/test_alias_initialization.py
@@ -1,10 +1,11 @@
-import gc
+import pytest
 
 
 def test_alias_delay_initialization1(capture):
-    """A only initializes its trampoline class when we inherit from it; if we just
-    create and use an A instance directly, the trampoline initialization is bypassed
-    and we only initialize an A() instead (for performance reasons).
+    """
+    A only initializes its trampoline class when we inherit from it; if we just
+    create and use an A instance directly, the trampoline initialization is
+    bypassed and we only initialize an A() instead (for performance reasons).
     """
     from pybind11_tests import A, call_f
 
@@ -20,7 +21,7 @@
         a = A()
         call_f(a)
         del a
-        gc.collect()
+        pytest.gc_collect()
     assert capture == "A.f()"
 
     # Python version
@@ -28,7 +29,7 @@
         b = B()
         call_f(b)
         del b
-        gc.collect()
+        pytest.gc_collect()
     assert capture == """
         PyA.PyA()
         PyA.f()
@@ -57,7 +58,7 @@
         a2 = A2()
         call_f(a2)
         del a2
-        gc.collect()
+        pytest.gc_collect()
     assert capture == """
         PyA2.PyA2()
         PyA2.f()
@@ -70,7 +71,7 @@
         b2 = B2()
         call_f(b2)
         del b2
-        gc.collect()
+        pytest.gc_collect()
     assert capture == """
         PyA2.PyA2()
         PyA2.f()
diff --git a/tests/test_buffers.cpp b/tests/test_buffers.cpp
index c3a7a9e..057250d 100644
--- a/tests/test_buffers.cpp
+++ b/tests/test_buffers.cpp
@@ -75,7 +75,7 @@
 };
 
 test_initializer buffers([](py::module &m) {
-    py::class_<Matrix> mtx(m, "Matrix");
+    py::class_<Matrix> mtx(m, "Matrix", py::buffer_protocol());
 
     mtx.def(py::init<size_t, size_t>())
         /// Construct from a buffer
diff --git a/tests/test_buffers.py b/tests/test_buffers.py
index f0ea964..956839c 100644
--- a/tests/test_buffers.py
+++ b/tests/test_buffers.py
@@ -6,34 +6,6 @@
 
 
 @pytest.requires_numpy
-def test_to_python():
-    m = Matrix(5, 5)
-
-    assert m[2, 3] == 0
-    m[2, 3] = 4
-    assert m[2, 3] == 4
-
-    m2 = np.array(m, copy=False)
-    assert m2.shape == (5, 5)
-    assert abs(m2).sum() == 4
-    assert m2[2, 3] == 4
-    m2[2, 3] = 5
-    assert m2[2, 3] == 5
-
-    cstats = ConstructorStats.get(Matrix)
-    assert cstats.alive() == 1
-    del m
-    assert cstats.alive() == 1
-    del m2  # holds an m reference
-    assert cstats.alive() == 0
-    assert cstats.values() == ["5x5 matrix"]
-    assert cstats.copy_constructions == 0
-    # assert cstats.move_constructions >= 0  # Don't invoke any
-    assert cstats.copy_assignments == 0
-    assert cstats.move_assignments == 0
-
-
-@pytest.requires_numpy
 def test_from_python():
     with pytest.raises(RuntimeError) as excinfo:
         Matrix(np.array([1, 2, 3]))  # trying to assign a 1D array
@@ -55,3 +27,36 @@
     # assert cstats.move_constructions >= 0  # Don't invoke any
     assert cstats.copy_assignments == 0
     assert cstats.move_assignments == 0
+
+
+# PyPy: Memory leak in the "np.array(m, copy=False)" call
+# https://bitbucket.org/pypy/pypy/issues/2444
+@pytest.unsupported_on_pypy
+@pytest.requires_numpy
+def test_to_python():
+    m = Matrix(5, 5)
+
+    assert m[2, 3] == 0
+    m[2, 3] = 4
+    assert m[2, 3] == 4
+
+    m2 = np.array(m, copy=False)
+    assert m2.shape == (5, 5)
+    assert abs(m2).sum() == 4
+    assert m2[2, 3] == 4
+    m2[2, 3] = 5
+    assert m2[2, 3] == 5
+
+    cstats = ConstructorStats.get(Matrix)
+    assert cstats.alive() == 1
+    del m
+    pytest.gc_collect()
+    assert cstats.alive() == 1
+    del m2  # holds an m reference
+    pytest.gc_collect()
+    assert cstats.alive() == 0
+    assert cstats.values() == ["5x5 matrix"]
+    assert cstats.copy_constructions == 0
+    # assert cstats.move_constructions >= 0  # Don't invoke any
+    assert cstats.copy_assignments == 0
+    assert cstats.move_assignments == 0
diff --git a/tests/test_issues.py b/tests/test_issues.py
index 2098ff8..e60b5ca 100644
--- a/tests/test_issues.py
+++ b/tests/test_issues.py
@@ -1,5 +1,4 @@
 import pytest
-import gc
 from pybind11_tests import ConstructorStats
 
 
@@ -55,7 +54,7 @@
     el = ElementList()
     for i in range(10):
         el.add(ElementA(i))
-    gc.collect()
+    pytest.gc_collect()
     for i, v in enumerate(el.get()):
         assert i == v.value()
 
@@ -130,13 +129,13 @@
     assert c.b.a.as_base().value == 42
 
     del c
-    gc.collect()
+    pytest.gc_collect()
     del a  # Should't delete while abase is still alive
-    gc.collect()
+    pytest.gc_collect()
 
     assert abase.value == 42
     del abase, b
-    gc.collect()
+    pytest.gc_collect()
 
 
 def test_move_fallback():
diff --git a/tests/test_keep_alive.py b/tests/test_keep_alive.py
index 0cef346..bfd7d40 100644
--- a/tests/test_keep_alive.py
+++ b/tests/test_keep_alive.py
@@ -1,4 +1,4 @@
-import gc
+import pytest
 
 
 def test_keep_alive_argument(capture):
@@ -9,14 +9,14 @@
     assert capture == "Allocating parent."
     with capture:
         p.addChild(Child())
-        gc.collect()
+        pytest.gc_collect()
     assert capture == """
         Allocating child.
         Releasing child.
     """
     with capture:
         del p
-        gc.collect()
+        pytest.gc_collect()
     assert capture == "Releasing parent."
 
     with capture:
@@ -24,11 +24,11 @@
     assert capture == "Allocating parent."
     with capture:
         p.addChildKeepAlive(Child())
-        gc.collect()
+        pytest.gc_collect()
     assert capture == "Allocating child."
     with capture:
         del p
-        gc.collect()
+        pytest.gc_collect()
     assert capture == """
         Releasing parent.
         Releasing child.
@@ -43,14 +43,14 @@
     assert capture == "Allocating parent."
     with capture:
         p.returnChild()
-        gc.collect()
+        pytest.gc_collect()
     assert capture == """
         Allocating child.
         Releasing child.
     """
     with capture:
         del p
-        gc.collect()
+        pytest.gc_collect()
     assert capture == "Releasing parent."
 
     with capture:
@@ -58,11 +58,11 @@
     assert capture == "Allocating parent."
     with capture:
         p.returnChildKeepAlive()
-        gc.collect()
+        pytest.gc_collect()
     assert capture == "Allocating child."
     with capture:
         del p
-        gc.collect()
+        pytest.gc_collect()
     assert capture == """
         Releasing parent.
         Releasing child.
@@ -77,11 +77,11 @@
     assert capture == "Allocating parent."
     with capture:
         p.returnNullChildKeepAliveChild()
-        gc.collect()
+        pytest.gc_collect()
     assert capture == ""
     with capture:
         del p
-        gc.collect()
+        pytest.gc_collect()
     assert capture == "Releasing parent."
 
     with capture:
@@ -89,9 +89,9 @@
     assert capture == "Allocating parent."
     with capture:
         p.returnNullChildKeepAliveParent()
-        gc.collect()
+        pytest.gc_collect()
     assert capture == ""
     with capture:
         del p
-        gc.collect()
+        pytest.gc_collect()
     assert capture == "Releasing parent."
diff --git a/tests/test_methods_and_attributes.cpp b/tests/test_methods_and_attributes.cpp
index 11fc900..824e743 100644
--- a/tests/test_methods_and_attributes.cpp
+++ b/tests/test_methods_and_attributes.cpp
@@ -134,10 +134,9 @@
         .def("overloaded_const", static_cast<py::str (ExampleMandA::*)(float, int) const>(&ExampleMandA::overloaded))
 #endif
         .def("__str__", &ExampleMandA::toString)
-        .def_readwrite("value", &ExampleMandA::value)
-        ;
+        .def_readwrite("value", &ExampleMandA::value);
 
-    py::class_<TestProperties>(m, "TestProperties")
+    py::class_<TestProperties>(m, "TestProperties", py::metaclass())
         .def(py::init<>())
         .def_readonly("def_readonly", &TestProperties::value)
         .def_readwrite("def_readwrite", &TestProperties::value)
@@ -160,7 +159,7 @@
     auto static_set2 = [](py::object, int v) { TestPropRVP::sv2.value = v; };
     auto rvp_copy = py::return_value_policy::copy;
 
-    py::class_<TestPropRVP>(m, "TestPropRVP")
+    py::class_<TestPropRVP>(m, "TestPropRVP", py::metaclass())
         .def(py::init<>())
         .def_property_readonly("ro_ref", &TestPropRVP::get1)
         .def_property_readonly("ro_copy", &TestPropRVP::get2, rvp_copy)
diff --git a/tests/test_methods_and_attributes.py b/tests/test_methods_and_attributes.py
index 2b0f8d5..1502f77 100644
--- a/tests/test_methods_and_attributes.py
+++ b/tests/test_methods_and_attributes.py
@@ -125,10 +125,19 @@
     instance = TestPropRVP()
     o = instance.rvalue
     assert o.value == 1
+
+
+def test_property_rvalue_policy_static():
+    """When returning an rvalue, the return value policy is automatically changed from
+    `reference(_internal)` to `move`. The following would not work otherwise.
+    """
+    from pybind11_tests import TestPropRVP
     o = TestPropRVP.static_rvalue
     assert o.value == 1
 
 
+# https://bitbucket.org/pypy/pypy/issues/2447
+@pytest.unsupported_on_pypy
 def test_dynamic_attributes():
     from pybind11_tests import DynamicClass, CppDerivedDynamicClass
 
diff --git a/tests/test_multiple_inheritance.cpp b/tests/test_multiple_inheritance.cpp
index 3cb12b6..c57cb85 100644
--- a/tests/test_multiple_inheritance.cpp
+++ b/tests/test_multiple_inheritance.cpp
@@ -10,7 +10,6 @@
 
 #include "pybind11_tests.h"
 
-
 struct Base1 {
     Base1(int i) : i(i) { }
     int foo() { return i; }
diff --git a/tests/test_multiple_inheritance.py b/tests/test_multiple_inheritance.py
index 581cf56..c10298d 100644
--- a/tests/test_multiple_inheritance.py
+++ b/tests/test_multiple_inheritance.py
@@ -1,5 +1,3 @@
-
-
 def test_multiple_inheritance_cpp():
     from pybind11_tests import MIType
 
diff --git a/tests/test_numpy_array.py b/tests/test_numpy_array.py
index 1c218a1..b96790c 100644
--- a/tests/test_numpy_array.py
+++ b/tests/test_numpy_array.py
@@ -1,5 +1,4 @@
 import pytest
-import gc
 
 with pytest.suppress(ImportError):
     import numpy as np
@@ -220,7 +219,7 @@
         ac_view_2 = ac.numpy_view()
         assert np.all(ac_view_1 == np.array([1, 2], dtype=np.int32))
         del ac
-        gc.collect()
+        pytest.gc_collect()
     assert capture == """
         ArrayClass()
         ArrayClass::numpy_view()
@@ -233,12 +232,14 @@
     with capture:
         del ac_view_1
         del ac_view_2
-        gc.collect()
+        pytest.gc_collect()
+        pytest.gc_collect()
     assert capture == """
         ~ArrayClass()
     """
 
 
+@pytest.unsupported_on_pypy
 @pytest.requires_numpy
 def test_cast_numpy_int64_to_uint64():
     from pybind11_tests.array import function_taking_uint64
diff --git a/tests/test_operator_overloading.py b/tests/test_operator_overloading.py
index e0d4239..02ccb96 100644
--- a/tests/test_operator_overloading.py
+++ b/tests/test_operator_overloading.py
@@ -1,4 +1,3 @@
-
 def test_operator_overloading():
     from pybind11_tests import Vector2, Vector, ConstructorStats
 
diff --git a/tests/test_pickling.py b/tests/test_pickling.py
index 5e62e1f..548c618 100644
--- a/tests/test_pickling.py
+++ b/tests/test_pickling.py
@@ -1,3 +1,5 @@
+import pytest
+
 try:
     import cPickle as pickle  # Use cPickle on Python 2.7
 except ImportError:
@@ -18,6 +20,7 @@
     assert p2.extra2() == p.extra2()
 
 
+@pytest.unsupported_on_pypy
 def test_roundtrip_with_dict():
     from pybind11_tests import PickleableWithDict
 
diff --git a/tests/test_python_types.cpp b/tests/test_python_types.cpp
index ae77f82..e1598e9 100644
--- a/tests/test_python_types.cpp
+++ b/tests/test_python_types.cpp
@@ -185,7 +185,7 @@
 test_initializer python_types([](py::module &m) {
     /* No constructor is explicitly defined below. An exception is raised when
        trying to construct it directly from Python */
-    py::class_<ExamplePythonTypes>(m, "ExamplePythonTypes", "Example 2 documentation")
+    py::class_<ExamplePythonTypes>(m, "ExamplePythonTypes", "Example 2 documentation", py::metaclass())
         .def("get_dict", &ExamplePythonTypes::get_dict, "Return a Python dictionary")
         .def("get_dict_2", &ExamplePythonTypes::get_dict_2, "Return a C++ dictionary")
         .def("get_list", &ExamplePythonTypes::get_list, "Return a Python list")
@@ -212,8 +212,7 @@
         .def("test_print", &ExamplePythonTypes::test_print, "test the print function")
         .def_static("new_instance", &ExamplePythonTypes::new_instance, "Return an instance")
         .def_readwrite_static("value", &ExamplePythonTypes::value, "Static value member")
-        .def_readonly_static("value2", &ExamplePythonTypes::value2, "Static value member (readonly)")
-        ;
+        .def_readonly_static("value2", &ExamplePythonTypes::value2, "Static value member (readonly)");
 
     m.def("test_print_function", []() {
         py::print("Hello, World!");
diff --git a/tests/test_python_types.py b/tests/test_python_types.py
index 9fe1ef7..347abaa 100644
--- a/tests/test_python_types.py
+++ b/tests/test_python_types.py
@@ -132,8 +132,12 @@
     assert cstats.alive() == 0
 
 
-def test_docs(doc):
+# PyPy does not seem to propagate the tp_docs field at the moment
+def test_class_docs(doc):
     assert doc(ExamplePythonTypes) == "Example 2 documentation"
+
+
+def test_method_docs(doc):
     assert doc(ExamplePythonTypes.get_dict) == """
         get_dict(self: m.ExamplePythonTypes) -> dict
 
diff --git a/tests/test_virtual_functions.py b/tests/test_virtual_functions.py
index a9aecd6..b11c699 100644
--- a/tests/test_virtual_functions.py
+++ b/tests/test_virtual_functions.py
@@ -206,6 +206,9 @@
     assert obj.say_everything() == "BT -7"
 
 
+# PyPy: Reference count > 1 causes call with noncopyable instance
+# to fail in ncv1.print_nc()
+@pytest.unsupported_on_pypy
 @pytest.mark.skipif(not hasattr(pybind11_tests, 'NCVirt'),
                     reason="NCVirt test broken on ICPC")
 def test_move_support():