diff --git a/tests/test_kwargs_and_defaults.py b/tests/test_kwargs_and_defaults.py
index 6c72a9368..531a9fdae 100644
--- a/tests/test_kwargs_and_defaults.py
+++ b/tests/test_kwargs_and_defaults.py
@@ -2,6 +2,11 @@
 import pytest
 from pybind11_tests import kwargs_and_defaults as m
 
+import platform
+import sys
+
+pypy = platform.python_implementation() == "PyPy"
+
 
 def test_function_signatures(doc):
     assert doc(m.kw_func0) == "kw_func0(arg0: int, arg1: int) -> str"
@@ -146,6 +151,8 @@ def test_keyword_only_args(msg):
     """
 
 
+@pytest.mark.xfail(pypy and sys.version_info < (3, 0),
+                   reason="PyPy2 doesn't seem to double count")
 def test_args_refcount():
     """Issue/PR #1216 - py::args elements get double-inc_ref()ed when combined with regular
     arguments"""
diff --git a/tests/test_pytypes.py b/tests/test_pytypes.py
index 5d2ccf8fd..4cfc707a3 100644
--- a/tests/test_pytypes.py
+++ b/tests/test_pytypes.py
@@ -322,7 +322,8 @@ def test_memoryview_from_buffer_empty_shape():
     assert view.format == 'B'
     if sys.version_info.major < 3:
         # Python 2 behavior is weird, but Python 3 (the future) is fine.
-        assert bytes(view).startswith(b'<memory at ')
+        # PyPy3 has <memoryview, while CPython 2 has <memory
+        assert bytes(view).startswith(b'<memory')
     else:
         assert bytes(view) == b''