diff --git a/bin/update_constraints b/bin/update_constraints
index 773a1d83..0e6ca9e4 100755
--- a/bin/update_constraints
+++ b/bin/update_constraints
@@ -20,7 +20,7 @@ subprocess.check_call([
     '--generate-hashes',
     '--upgrade',
     'cibuildwheel/resources/constraints.in',
-    '--output-file', 'cibuildwheel/resources/constraints-python2.txt'
+    '--output-file', 'cibuildwheel/resources/constraints-python27.txt'
 ])
 
 Image = namedtuple('Image', ['manylinux_version', 'arch'])
diff --git a/cibuildwheel/__main__.py b/cibuildwheel/__main__.py
index 890bd4c7..38ecd711 100644
--- a/cibuildwheel/__main__.py
+++ b/cibuildwheel/__main__.py
@@ -4,7 +4,7 @@ import argparse, os, subprocess, sys, textwrap
 import cibuildwheel
 import cibuildwheel.linux, cibuildwheel.windows, cibuildwheel.macos
 from cibuildwheel.environment import parse_environment, EnvironmentParseError
-from cibuildwheel.util import BuildSelector, Unbuffered
+from cibuildwheel.util import BuildSelector, DependencyConstraints, Unbuffered
 
 def get_option_from_environment(option_name, platform=None, default=None):
     '''
@@ -102,15 +102,14 @@ def main():
         repair_command_default = ''
     repair_command = get_option_from_environment('CIBW_REPAIR_WHEEL_COMMAND', platform=platform, default=repair_command_default)
     environment_config = get_option_from_environment('CIBW_ENVIRONMENT', platform=platform, default='')
+
     dependency_versions = get_option_from_environment('CIBW_DEPENDENCY_VERSIONS', platform=platform, default='pinned')
     if dependency_versions == 'pinned':
-        dependency_constraints = os.path.join(
-            os.path.dirname(__file__), 'resources', 'constraints.txt'
-        )
+        dependency_constraints = DependencyConstraints.with_defaults()
     elif dependency_versions == 'latest':
-        dependency_constraints = ''
+        dependency_constraints = None
     else:
-        dependency_constraints = dependency_versions
+        dependency_constraints = DependencyConstraints(dependency_versions)
 
     if test_extras:
         test_extras = '[{0}]'.format(test_extras)
diff --git a/cibuildwheel/linux.py b/cibuildwheel/linux.py
index ebbd9dc4..db066394 100644
--- a/cibuildwheel/linux.py
+++ b/cibuildwheel/linux.py
@@ -10,20 +10,20 @@ except ImportError:
 
 
 def get_python_configurations(build_selector):
-    PythonConfiguration = namedtuple('PythonConfiguration', ['identifier', 'path'])
+    PythonConfiguration = namedtuple('PythonConfiguration', ['version', 'identifier', 'path'])
     python_configurations = [
-        PythonConfiguration(identifier='cp27-manylinux_x86_64', path='/opt/python/cp27-cp27m'),
-        PythonConfiguration(identifier='cp27-manylinux_x86_64', path='/opt/python/cp27-cp27mu'),
-        PythonConfiguration(identifier='cp35-manylinux_x86_64', path='/opt/python/cp35-cp35m'),
-        PythonConfiguration(identifier='cp36-manylinux_x86_64', path='/opt/python/cp36-cp36m'),
-        PythonConfiguration(identifier='cp37-manylinux_x86_64', path='/opt/python/cp37-cp37m'),
-        PythonConfiguration(identifier='cp38-manylinux_x86_64', path='/opt/python/cp38-cp38'),
-        PythonConfiguration(identifier='cp27-manylinux_i686', path='/opt/python/cp27-cp27m'),
-        PythonConfiguration(identifier='cp27-manylinux_i686', path='/opt/python/cp27-cp27mu'),
-        PythonConfiguration(identifier='cp35-manylinux_i686', path='/opt/python/cp35-cp35m'),
-        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(version='2.7', identifier='cp27-manylinux_x86_64', path='/opt/python/cp27-cp27m'),
+        PythonConfiguration(version='2.7', identifier='cp27-manylinux_x86_64', path='/opt/python/cp27-cp27mu'),
+        PythonConfiguration(version='3.5', identifier='cp35-manylinux_x86_64', path='/opt/python/cp35-cp35m'),
+        PythonConfiguration(version='3.6', identifier='cp36-manylinux_x86_64', path='/opt/python/cp36-cp36m'),
+        PythonConfiguration(version='3.7', identifier='cp37-manylinux_x86_64', path='/opt/python/cp37-cp37m'),
+        PythonConfiguration(version='3.8', identifier='cp38-manylinux_x86_64', path='/opt/python/cp38-cp38'),
+        PythonConfiguration(version='2.7', identifier='cp27-manylinux_i686', path='/opt/python/cp27-cp27m'),
+        PythonConfiguration(version='2.7', identifier='cp27-manylinux_i686', path='/opt/python/cp27-cp27mu'),
+        PythonConfiguration(version='3.5', identifier='cp35-manylinux_i686', path='/opt/python/cp35-cp35m'),
+        PythonConfiguration(version='3.6', identifier='cp36-manylinux_i686', path='/opt/python/cp36-cp36m'),
+        PythonConfiguration(version='3.7', identifier='cp37-manylinux_i686', path='/opt/python/cp37-cp37m'),
+        PythonConfiguration(version='3.8', identifier='cp38-manylinux_i686', path='/opt/python/cp38-cp38'),
     ]
 
     # skip builds as required
@@ -79,7 +79,9 @@ def build(project_dir, output_dir, test_command, test_requires, test_extras, bef
 
             for config in platform_configs:
                 if dependency_constraints:
-                    run_docker(['cp', os.path.abspath(dependency_constraints), container_name + ':/constraints.txt'])
+                    constraints_file = dependency_constraints.get_for_python_version(config.version)
+                    run_docker(['cp', os.path.abspath(constraints_file), container_name + ':/constraints.txt'])
+
                 run_docker(['start', '-i', '-a', container_name], stdin_str='''
                     set -o errexit
                     set -o xtrace
diff --git a/cibuildwheel/macos.py b/cibuildwheel/macos.py
index 0a221b29..72b45426 100644
--- a/cibuildwheel/macos.py
+++ b/cibuildwheel/macos.py
@@ -87,7 +87,11 @@ def build(project_dir, output_dir, test_command, test_requires, test_extras, bef
         call(['which', 'python'], env=env)
         call(['python', '--version'], env=env)
 
-        dependency_constraint_flags = ['-c', dependency_constraints] if dependency_constraints else []
+        dependency_constraint_flags = []
+        if dependency_constraints:
+            dependency_constraint_flags = [
+                '-c', dependency_constraints.get_for_python_version(config.version)
+            ]
 
         # install pip & wheel
         call(['python', get_pip_script, '--no-setuptools', '--no-wheel'] + dependency_constraint_flags, env=env, cwd="/tmp")
diff --git a/cibuildwheel/resources/constraints-python27.txt b/cibuildwheel/resources/constraints-python27.txt
new file mode 100644
index 00000000..19b904ee
--- /dev/null
+++ b/cibuildwheel/resources/constraints-python27.txt
@@ -0,0 +1,29 @@
+#
+# This file is autogenerated by pip-compile
+# To update, run:
+#
+#    bin/update_constraints
+#
+auditwheel==2.1.1 \
+    --hash=sha256:d9f0f47c0ecdf4f72316eabfb19223b81aec95f0deba97729e9c09ea4f2c166e \
+    --hash=sha256:f60e265dc168ae7c9d65a814410881c5ca170d88644c178f8e3aa20eecd0fae1
+delocate==0.8.0 \
+    --hash=sha256:ac9f4d8d28b2582d94f764db0d72a1fe3c42ab8212e9b780168455de385d5b95
+pyelftools==0.26 \
+    --hash=sha256:86ac6cee19f6c945e8dedf78c6ee74f1112bd14da5a658d8c9d4103aed5756a2 \
+    --hash=sha256:cc0ea0de82b240a73ef4056fce44acbb4727dca7d66759371aff2bad457ed711 \
+    # via auditwheel
+virtualenv==16.7.9 \
+    --hash=sha256:0d62c70883c0342d59c11d0ddac0d954d0431321a41ab20851facf2b222598f3 \
+    --hash=sha256:55059a7a676e4e19498f1aad09b8313a38fcc0cdbe4fdddc0e9b06946d21b4bb
+wheel==0.31.1 \
+    --hash=sha256:0a2e54558a0628f2145d2fc822137e322412115173e8a2ddbe1c9024338ae83c \
+    --hash=sha256:80044e51ec5bbf6c894ba0bc48d26a8c20a9ba629f4ca19ea26ecfcf87685f5f
+
+# The following packages are considered to be unsafe in a requirements file:
+pip==20.0.2 \
+    --hash=sha256:4ae14a42d8adba3205ebeb38aa68cfc0b6c346e1ae2e699a0b3bad4da19cef5c \
+    --hash=sha256:7db0c8ea4c7ea51c8049640e8e6e7fde949de672bfa4949920675563a5a6967f
+setuptools==44.0.0 \
+    --hash=sha256:180081a244d0888b0065e18206950d603f6550721bd6f8c0a10221ed467dd78e \
+    --hash=sha256:e5baf7723e5bb8382fc146e33032b241efc63314211a3a120aaa55d62d2bb008
diff --git a/cibuildwheel/util.py b/cibuildwheel/util.py
index 7d67d436..28648a18 100644
--- a/cibuildwheel/util.py
+++ b/cibuildwheel/util.py
@@ -83,4 +83,29 @@ def download(url, dest):
         response.close()
 
 
+class DependencyConstraints(object):
+    def __init__(self, base_file_path):
+        assert os.path.exists(base_file_path)
+        self.base_file_path = base_file_path
+
+    @classmethod
+    def with_defaults(cls):
+        return cls(
+            base_file_path=os.path.join(os.path.dirname(__file__), 'resources', 'constraints.txt')
+        )
+
+    def get_for_python_version(self, version):
+        version_parts = version.split('.')
+
+        # try to find a version-specific dependency file e.g. if
+        # ./constraints.txt is the base, look for ./constraints-python27.txt
+        base, ext = os.path.splitext(self.base_file_path)
+        specific = base + '-{}{}'.format(version_parts[0], version_parts[1])
+        specific_file_path = specific + ext
+        if os.path.exists(specific_file_path):
+            return specific_file_path
+        else:
+            return self.base_file_path
+
+
 get_pip_script = os.path.abspath(os.path.join(os.path.dirname(__file__), 'resources', 'get-pip.py'))
diff --git a/cibuildwheel/windows.py b/cibuildwheel/windows.py
index b4e612d0..141b5049 100644
--- a/cibuildwheel/windows.py
+++ b/cibuildwheel/windows.py
@@ -104,8 +104,12 @@ def build(project_dir, output_dir, test_command, test_requires, test_extras, bef
         simple_shell(['python', '--version'], env=env)
         simple_shell(['python', '-c', '"import struct; print(struct.calcsize(\'P\') * 8)\"'], env=env)
 
-        dependency_constraint_flags = ['-c', dependency_constraints] if dependency_constraints else []
-                    
+        dependency_constraint_flags = []
+        if dependency_constraints:
+            dependency_constraint_flags = [
+                '-c', dependency_constraints.get_for_python_version(config.version)
+            ]
+
         # make sure pip is installed
         if not os.path.exists(os.path.join(config_python_path, 'Scripts', 'pip.exe')):
             simple_shell(['python', get_pip_script] + dependency_constraint_flags, env=env, cwd="C:\\cibw")
diff --git a/docs/options.md b/docs/options.md
index f32305ed..919837d4 100644
--- a/docs/options.md
+++ b/docs/options.md
@@ -285,6 +285,13 @@ To control the versions of dependencies yourself, you can supply a [pip
 constraints](https://pip.pypa.io/en/stable/user_guide/#constraints-files) file
 here and it will be used instead.
 
+!!! note
+    If you need different dependencies for each python version, provide them
+    in the same folder with a `-pythonXY` suffix. e.g. if your
+    `CIBW_DEPENDENCY_VERSIONS=./constraints.txt`, cibuildwheel will use
+    `./constraints-python27.txt` on Python 2.7, or fallback to
+    `./constraints.txt` if that's not found.
+
 Platform-specific variants also available:<br/>
 `CIBW_DEPENDENCY_VERSIONS_MACOS` | `CIBW_DEPENDENCY_VERSIONS_WINDOWS` | `CIBW_DEPENDENCY_VERSIONS_LINUX`