diff --git a/cibuildwheel/macos.py b/cibuildwheel/macos.py
index 9173849e..8eb7984c 100644
--- a/cibuildwheel/macos.py
+++ b/cibuildwheel/macos.py
@@ -36,8 +36,8 @@ def get_python_configurations(build_selector):
         PythonConfiguration(version='3.7', identifier='cp37-macosx_x86_64', url='https://www.python.org/ftp/python/3.7.7/python-3.7.7-macosx10.9.pkg'),
         PythonConfiguration(version='3.8', identifier='cp38-macosx_x86_64', url='https://www.python.org/ftp/python/3.8.2/python-3.8.2-macosx10.9.pkg'),
         # PyPy
-        PythonConfiguration(version='2.7', identifier='pp27-macosx_x86_64', url='https://bitbucket.org/pypy/pypy/downloads/pypy2.7-v7.3.0-osx64.tar.bz2'),
-        PythonConfiguration(version='3.6', identifier='pp36-macosx_x86_64', url='https://bitbucket.org/pypy/pypy/downloads/pypy3.6-v7.3.0-osx64.tar.bz2'),
+        PythonConfiguration(version='2.7', identifier='pp27-macosx_x86_64', url='https://downloads.python.org/pypy/pypy2.7-v7.3.1-osx64.tar.bz2'),
+        PythonConfiguration(version='3.6', identifier='pp36-macosx_x86_64', url='https://downloads.python.org/pypy/pypy3.6-v7.3.1-osx64.tar.bz2'),
     ]
 
     # skip builds as required
@@ -95,12 +95,6 @@ def install_pypy(version, url):
         download(url, os.path.join("/tmp", pypy_tar_bz2))
         call(['tar', '-C', '/tmp', '-xf', os.path.join("/tmp", pypy_tar_bz2)])
 
-        # fix PyPy 7.3.0 bug resulting in wrong macOS platform tag
-        if "-v7.3.0-" in url and version[0] == '3':
-            patch_file = os.path.abspath(os.path.join(os.path.dirname(__file__), 'resources', 'pypy3.6.patch'))
-            sysconfigdata_file = os.path.join(installation_path, 'lib_pypy', '_sysconfigdata.py')
-            call(['patch', sysconfigdata_file, patch_file, '-N'])  # Always has nonzero return code
-
     installation_bin_path = os.path.join(installation_path, 'bin')
     python_executable = 'pypy3' if version[0] == '3' else 'pypy'
     pip_executable = 'pip3' if version[0] == '3' else 'pip'
diff --git a/cibuildwheel/resources/pinned_docker_images.cfg b/cibuildwheel/resources/pinned_docker_images.cfg
index 7cbcab64..084bb6e6 100644
--- a/cibuildwheel/resources/pinned_docker_images.cfg
+++ b/cibuildwheel/resources/pinned_docker_images.cfg
@@ -9,7 +9,7 @@ manylinux2010 = quay.io/pypa/manylinux2010_i686:2020-03-07-1825e8f
 manylinux2014 = quay.io/pypa/manylinux2014_i686:2020-03-07-06139da
 
 [pypy_x86_64]
-manylinux2010 = pypywheels/manylinux2010-pypy_x86_64:latest
+manylinux2010 = pypywheels/manylinux2010-pypy_x86_64:2020-04-15-4ce2a6f
 
 [aarch64]
 manylinux2014 = quay.io/pypa/manylinux2014_aarch64:2020-03-07-06139da
diff --git a/cibuildwheel/windows.py b/cibuildwheel/windows.py
index 8878d588..06efa255 100644
--- a/cibuildwheel/windows.py
+++ b/cibuildwheel/windows.py
@@ -47,8 +47,8 @@ def get_python_configurations(build_selector):
         PythonConfiguration(version='3.8.2', arch='32', identifier='cp38-win32', url=None),
         PythonConfiguration(version='3.8.2', arch='64', identifier='cp38-win_amd64', url=None),
         # PyPy
-        PythonConfiguration(version='2.7', arch='32', identifier='pp27-win32', url='https://bitbucket.org/pypy/pypy/downloads/pypy2.7-v7.3.0-win32.zip'),
-        PythonConfiguration(version='3.6', arch='32', identifier='pp36-win32', url='https://bitbucket.org/pypy/pypy/downloads/pypy3.6-v7.3.0-win32.zip'),
+        PythonConfiguration(version='2.7', arch='32', identifier='pp27-win32', url='https://downloads.python.org/pypy/pypy2.7-v7.3.1-win32.zip'),
+        PythonConfiguration(version='3.6', arch='32', identifier='pp36-win32', url='https://downloads.python.org/pypy/pypy3.6-v7.3.1-win32.zip'),
     ]
 
     if IS_RUNNING_ON_TRAVIS:
@@ -86,7 +86,6 @@ def install_pypy(version, arch, url):
         extract_zip(pypy_zip, os.path.dirname(installation_path))
         pypy_exe = 'pypy3.exe' if version[0] == '3' else 'pypy.exe'
         shell(['mklink', os.path.join(installation_path, 'python.exe'), os.path.join(installation_path, pypy_exe)])
-        shell(['mklink', '/d', os.path.join(installation_path, 'Scripts'), os.path.join(installation_path, 'bin')])
     return installation_path