diff --git a/cibuildwheel/linux.py b/cibuildwheel/linux.py
index 91339201b..35d588c7d 100644
--- a/cibuildwheel/linux.py
+++ b/cibuildwheel/linux.py
@@ -18,8 +18,8 @@ def get_python_configurations(build_selector):
         PythonConfiguration(identifier='cp36-manylinux_i686', path='/opt/python/cp36-cp36m'),
         PythonConfiguration(identifier='cp37-manylinux_i686', path='/opt/python/cp37-cp37m'),
         PythonConfiguration(identifier='cp38-manylinux_i686', path='/opt/python/cp38-cp38'),
-        PythonConfiguration(identifier='pp27_73-manylinux_x86_64', path='/opt/python/pp273-pypy_73'),
-        PythonConfiguration(identifier='pp36_73-manylinux_x86_64', path='/opt/python/pp373-pypy36_pp73'),
+        PythonConfiguration(identifier='pp27-manylinux_x86_64', path='/opt/python/pp273-pypy_73'),
+        PythonConfiguration(identifier='pp36-manylinux_x86_64', path='/opt/python/pp373-pypy36_pp73'),
     ]
 
     # skip builds as required
diff --git a/cibuildwheel/macos.py b/cibuildwheel/macos.py
index aff883979..4e4bccb68 100644
--- a/cibuildwheel/macos.py
+++ b/cibuildwheel/macos.py
@@ -24,8 +24,8 @@ def get_python_configurations(build_selector):
         PythonConfiguration(version='3.6', identifier='cp36-macosx_x86_64', url='https://www.python.org/ftp/python/3.6.8/python-3.6.8-macosx10.9.pkg'),
         PythonConfiguration(version='3.7', identifier='cp37-macosx_x86_64', url='https://www.python.org/ftp/python/3.7.6/python-3.7.6-macosx10.9.pkg'),
         PythonConfiguration(version='3.8', identifier='cp38-macosx_x86_64', url='https://www.python.org/ftp/python/3.8.1/python-3.8.1-macosx10.9.pkg'),
-        PythonConfiguration(version='2.7-v7.3.0', identifier='pp27_73-macosx_x86_64', url='https://bitbucket.org/pypy/pypy/downloads/pypy2.7-v7.3.0-osx64.tar.bz2'),
-        PythonConfiguration(version='3.6-v7.3.0', identifier='pp36_73-macosx_x86_64', url='https://bitbucket.org/pypy/pypy/downloads/pypy3.6-v7.3.0-osx64.tar.bz2'),
+        PythonConfiguration(version='2.7-v7.3.0', identifier='pp27-macosx_x86_64', url='https://bitbucket.org/pypy/pypy/downloads/pypy2.7-v7.3.0-osx64.tar.bz2'),
+        PythonConfiguration(version='3.6-v7.3.0', identifier='pp36-macosx_x86_64', url='https://bitbucket.org/pypy/pypy/downloads/pypy3.6-v7.3.0-osx64.tar.bz2'),
     ]
 
     # skip builds as required
diff --git a/cibuildwheel/windows.py b/cibuildwheel/windows.py
index e082357b8..05e0d5950 100644
--- a/cibuildwheel/windows.py
+++ b/cibuildwheel/windows.py
@@ -50,8 +50,8 @@ def get_python_configurations(build_selector):
         PythonConfiguration(version='3.7.6', arch='64', identifier='cp37-win_amd64', url=None),
         PythonConfiguration(version='3.8.1', arch='32', identifier='cp38-win32', url=None),
         PythonConfiguration(version='3.8.1', arch='64', identifier='cp38-win_amd64', url=None),
-        PythonConfiguration(version='2.7-v7.3.0', arch='32', identifier='pp27_73-win32', url='https://bitbucket.org/pypy/pypy/downloads/pypy2.7-v7.3.0-win32.zip'),
-        PythonConfiguration(version='3.6-v7.3.0', arch='32', identifier='pp36_73-win32', url='https://bitbucket.org/pypy/pypy/downloads/pypy3.6-v7.3.0-win32.zip'),
+        PythonConfiguration(version='2.7-v7.3.0', arch='32', identifier='pp27-win32', url='https://bitbucket.org/pypy/pypy/downloads/pypy2.7-v7.3.0-win32.zip'),
+        PythonConfiguration(version='3.6-v7.3.0', arch='32', identifier='pp36-win32', url='https://bitbucket.org/pypy/pypy/downloads/pypy3.6-v7.3.0-win32.zip'),
     ]
 
     if IS_RUNNING_ON_TRAVIS:
diff --git a/docs/options.md b/docs/options.md
index f6b744381..5da4554cd 100644
--- a/docs/options.md
+++ b/docs/options.md
@@ -72,15 +72,15 @@ When setting the options, you can use shell-style globbing syntax (as per [`fnma
 
 <div class="build-id-table-marker"></div>
 
-|                 | macOS 64bit            | Manylinux 64bit           | Manylinux 32bit      | Windows 64bit   | Windows 32bit  |
-|-----------------|------------------------|---------------------------|----------------------|-----------------|----------------|
-| Python 2.7      | cp27-macosx_x86_64     | cp27-manylinux_x86_64     | cp27-manylinux_i686  | cp27-win_amd64  | cp27-win32     |
-| Python 3.5      | cp35-macosx_x86_64     | cp35-manylinux_x86_64     | cp35-manylinux_i686  | cp35-win_amd64  | cp35-win32     |
-| Python 3.6      | cp36-macosx_x86_64     | cp36-manylinux_x86_64     | cp36-manylinux_i686  | cp36-win_amd64  | cp36-win32     |
-| Python 3.7      | cp37-macosx_x86_64     | cp37-manylinux_x86_64     | cp37-manylinux_i686  | cp37-win_amd64  | cp37-win32     |
-| Python 3.8      | cp38-macosx_x86_64     | cp38-manylinux_x86_64     | cp38-manylinux_i686  | cp38-win_amd64  | cp38-win32     |
-| PyPy 2.7 v7.3.0 | pp27_73-macosx_x86_64  | pp27_73-manylinux_x86_64  |                      |                 | pp27_73-win32  |
-| PyPy 3.6 v7.3.0 | pp36_73-macosx_x86_64  | pp36_73-manylinux_x86_64  |                      |                 | pp36_73-win32  |
+|                 | macOS 64bit         | Manylinux 64bit        | Manylinux 32bit      | Windows 64bit   | Windows 32bit  |
+|-----------------|---------------------|------------------------|----------------------|-----------------|----------------|
+| Python 2.7      | cp27-macosx_x86_64  | cp27-manylinux_x86_64  | cp27-manylinux_i686  | cp27-win_amd64  | cp27-win32     |
+| Python 3.5      | cp35-macosx_x86_64  | cp35-manylinux_x86_64  | cp35-manylinux_i686  | cp35-win_amd64  | cp35-win32     |
+| Python 3.6      | cp36-macosx_x86_64  | cp36-manylinux_x86_64  | cp36-manylinux_i686  | cp36-win_amd64  | cp36-win32     |
+| Python 3.7      | cp37-macosx_x86_64  | cp37-manylinux_x86_64  | cp37-manylinux_i686  | cp37-win_amd64  | cp37-win32     |
+| Python 3.8      | cp38-macosx_x86_64  | cp38-manylinux_x86_64  | cp38-manylinux_i686  | cp38-win_amd64  | cp38-win32     |
+| PyPy 2.7 v7.3.0 | pp27-macosx_x86_64  | pp27-manylinux_x86_64  |                      |                 | pp27-win32     |
+| PyPy 3.6 v7.3.0 | pp36-macosx_x86_64  | pp36-manylinux_x86_64  |                      |                 | pp36-win32     |
 
 The list of supported and currently selected build identifiers can also be retrieved by passing the `--print-build-identifiers` flag to `cibuildwheel`.
 The format is `python_tag-platform_tag`, with tags similar to those in [PEP 425](https://www.python.org/dev/peps/pep-0425/#details).
@@ -119,7 +119,7 @@ CIBW_BUILD: cp3?-*
 CIBW_SKIP: "*-win32 *-manylinux_i686"
 
 # Only build PyPy and CPython 3
-CIBW_BUILD: pp*-* cp3?-*
+CIBW_BUILD: pp* cp3?-*
 ```
 
 <style>
@@ -262,7 +262,7 @@ Note that `manylinux2014` doesn't support builds with Python 2.7 - when building
 # skip PyPy, since there is no PyPy manylinux1 image
 CIBW_MANYLINUX_X86_64_IMAGE: manylinux1
 CIBW_MANYLINUX_I686_IMAGE: manylinux1
-CIBW_SKIP: pp*-*
+CIBW_SKIP: pp*
 
 # build using the manylinux2014 image
 CIBW_MANYLINUX_X86_64_IMAGE: manylinux2014
diff --git a/test/06_docker_images/cibuildwheel_test.py b/test/06_docker_images/cibuildwheel_test.py
index 9b2395f36..7160d2d2f 100644
--- a/test/06_docker_images/cibuildwheel_test.py
+++ b/test/06_docker_images/cibuildwheel_test.py
@@ -10,7 +10,7 @@ def test():
     actual_wheels = utils.cibuildwheel_run(project_dir, add_env={
         'CIBW_MANYLINUX_X86_64_IMAGE': 'dockcross/manylinux2010-x64',
         'CIBW_MANYLINUX_I686_IMAGE': 'dockcross/manylinux2010-x86',
-        'CIBW_SKIP': 'pp*-*',
+        'CIBW_SKIP': 'pp*',
     })
 
     # also check that we got the right wheels built
diff --git a/test/10_cpp_standards/cibuildwheel_test.py b/test/10_cpp_standards/cibuildwheel_test.py
index 6974828dd..4fdf8567f 100644
--- a/test/10_cpp_standards/cibuildwheel_test.py
+++ b/test/10_cpp_standards/cibuildwheel_test.py
@@ -11,7 +11,7 @@
 def test_cpp11(tmp_path):
     # This test checks that the C++11 standard is supported
 
-    add_env = {'CIBW_SKIP': 'cp27-win* pp27_73-win32', 'CIBW_ENVIRONMENT': 'STANDARD=11'}
+    add_env = {'CIBW_SKIP': 'cp27-win* pp27-win32', 'CIBW_ENVIRONMENT': 'STANDARD=11'}
     # VC++ for Python 2.7 does not support modern standards
     if utils.platform == 'macos':
         add_env['MACOSX_DEPLOYMENT_TARGET'] = '10.9'
@@ -27,7 +27,7 @@ def test_cpp11(tmp_path):
 def test_cpp14():
     # This test checks that the C++14 standard is supported
 
-    add_env = {'CIBW_SKIP': 'cp27-win* pp27_73-win32 cp35-win*', 'CIBW_ENVIRONMENT': 'STANDARD=14'}
+    add_env = {'CIBW_SKIP': 'cp27-win* pp27-win32 cp35-win*', 'CIBW_ENVIRONMENT': 'STANDARD=14'}
     # VC++ for Python 2.7 does not support modern standards
     # The manylinux1 docker image does not have a compiler which supports C++11
     # Python 3.4 and 3.5 are compiled with MSVC 10, which does not support C++14
@@ -52,7 +52,7 @@ def test_cpp17():
     if os.environ.get('APPVEYOR_BUILD_WORKER_IMAGE', '') == 'Visual Studio 2015':
         pytest.skip('Visual Studio 2015 does not support C++17')
 
-    add_env = {'CIBW_SKIP': 'cp27-win* pp27_73-win32 cp35-win* pp36_73-win32', 'CIBW_ENVIRONMENT': 'STANDARD=17'}
+    add_env = {'CIBW_SKIP': 'cp27-win* pp27-win32 cp35-win* pp36-win32', 'CIBW_ENVIRONMENT': 'STANDARD=17'}
     if utils.platform == 'macos':
         add_env['MACOSX_DEPLOYMENT_TARGET'] = '10.13'