diff --git a/pex/pep425.py b/pex/pep425.py
index 6689f6ec7..a859b13d0 100644
--- a/pex/pep425.py
+++ b/pex/pep425.py
@@ -99,15 +99,19 @@ def _iter_supported_tags(cls, impl, version, platform):
     """
     # Predict soabi for reasonable interpreters.  This is technically wrong but essentially right.
     abis = []
-    if impl == 'cp' and version.startswith('3'):
+    if impl == 'cp' and (version.startswith('2') or version.startswith('3')):
       abis.extend([
         'cp%s' % version,
         'cp%sdmu' % version, 'cp%sdm' % version, 'cp%sdu' % version, 'cp%sd' % version,
         'cp%smu' % version, 'cp%sm' % version,
-        'cp%su' % version,
-        'abi3'
+        'cp%su' % version
       ])
 
+      if version.startswith('3'):
+        abis.extend([
+          'abi3'
+        ])
+
     major_version = int(version[0])
     minor_versions = []
     for minor in range(int(version[1]), -1, -1):
diff --git a/tests/test_pep425.py b/tests/test_pep425.py
index 87caedde7..1b8ca36fb 100644
--- a/tests/test_pep425.py
+++ b/tests/test_pep425.py
@@ -46,6 +46,18 @@ def iter_solutions():
     for interp in ('cp', 'py'):
       for interp_suffix in ('2', '20', '21', '22', '23', '24', '25', '26'):
         for platform in ('linux_x86_64', 'any'):
-          yield (interp + interp_suffix, 'none', platform)
+          abis = ['none']
+
+          if interp == 'cp' and interp_suffix == '26' and platform == 'linux_x86_64':
+            abis.extend([
+              'cp%s' % interp_suffix,
+              'cp%sdmu' % interp_suffix, 'cp%sdm' % interp_suffix,
+              'cp%sdu' % interp_suffix, 'cp%sd' % interp_suffix,
+              'cp%smu' % interp_suffix, 'cp%sm' % interp_suffix,
+              'cp%su' % interp_suffix
+            ])
+
+          for abi in abis:
+            yield (interp + interp_suffix, abi, platform)
 
   assert set(PEP425.iter_supported_tags(identity, platform)) == set(iter_solutions())