diff --git a/cibuildwheel/resources/constraints-python2.txt b/cibuildwheel/resources/constraints-python2.txt
deleted file mode 100644
index 19b904ee..00000000
--- a/cibuildwheel/resources/constraints-python2.txt
+++ /dev/null
@@ -1,29 +0,0 @@
-#
-# 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 28648a18..aade60b2 100644
--- a/cibuildwheel/util.py
+++ b/cibuildwheel/util.py
@@ -100,7 +100,7 @@ class DependencyConstraints(object):
         # 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 = base + '-python{}{}'.format(version_parts[0], version_parts[1])
         specific_file_path = specific + ext
         if os.path.exists(specific_file_path):
             return specific_file_path
diff --git a/unit_test/dependency_constraints_test.py b/unit_test/dependency_constraints_test.py
new file mode 100644
index 00000000..2f6b3ccc
--- /dev/null
+++ b/unit_test/dependency_constraints_test.py
@@ -0,0 +1,21 @@
+from cibuildwheel.util import DependencyConstraints
+import os
+
+def test_defaults():
+    dependency_constraints = DependencyConstraints.with_defaults()
+
+    project_root = os.path.dirname(os.path.dirname(__file__))
+    resources_dir = os.path.join(project_root, 'cibuildwheel', 'resources')
+
+    assert os.path.samefile(
+        dependency_constraints.base_file_path,
+        os.path.join(resources_dir, 'constraints.txt')
+    )
+    assert os.path.samefile(
+        dependency_constraints.get_for_python_version('3.8'),
+        os.path.join(resources_dir, 'constraints.txt')
+    )
+    assert os.path.samefile(
+        dependency_constraints.get_for_python_version('2.7'),
+        os.path.join(resources_dir, 'constraints-python27.txt')
+    )