diff --git a/Lib/packaging/tests/test_pypi_dist.py b/Lib/packaging/tests/test_pypi_dist.py
--- a/Lib/packaging/tests/test_pypi_dist.py
+++ b/Lib/packaging/tests/test_pypi_dist.py
@@ -6,6 +6,7 @@
 from packaging.pypi.dist import (ReleaseInfo, ReleasesList, DistInfo,
                                  split_archive_name, get_infos_from_url)
 from packaging.pypi.errors import HashDoesNotMatch, UnsupportedHashName
+from packaging.errors import IrrationalVersionError
 
 from packaging.tests import unittest
 from packaging.tests.support import TempdirManager, requires_zlib, fake_dec
@@ -87,6 +88,31 @@
         for name, results in names.items():
             self.assertEqual(results, split_archive_name(name))
 
+    def test_irrational_version__normalization(self):
+        # Test irrational but normalizable (suggested) versions
+        normalizable = {
+            "0.4.5dev": "0.4.5.dev0",
+            "1.3.a4": "1.3a4",
+            "2.4-rc1": "2.4c1",
+            "1.2a": "1.2a0",
+            "1.2.3b": "1.2.3b0",
+            "1.02": "1.2",
+            "1.2a3.04": "1.2a3.4",
+            "1.2.dev.2": "1.2.dev2",
+            "1.2dev": "1.2.dev0",
+        }
+        for irrational, normalized in normalizable.items():
+            release = ReleaseInfo("FooBar", irrational)
+            self.assertEqual(normalized, str(release.version))
+
+    def test_irrational_and_not_normalizable_versions(self):
+        # Test irrational/invalid versions that are NOT normalizable
+        irrational = ("abc", "aa bb", "1", "1.3pl1", "1.2a03",
+                      "1.2.dev2.post2", "1.2.post2.dev3.post4")
+        for version in irrational:
+            self.assertRaises(IrrationalVersionError, ReleaseInfo, "FooBar",
+                              version)
+
 
 class TestDistInfo(TempdirManager, unittest.TestCase):
     srcpath = "/packages/source/f/foobar/foobar-0.1.tar.gz"