diff --git a/packaging/specifiers.py b/packaging/specifiers.py
index 9f7dd278..fe09bb1d 100644
--- a/packaging/specifiers.py
+++ b/packaging/specifiers.py
@@ -516,12 +516,20 @@ def _compare_not_equal(self, prospective, spec):
     @_require_version_compare
     def _compare_less_than_equal(self, prospective, spec):
         # type: (ParsedVersion, str) -> bool
-        return prospective <= Version(spec)
+
+        # NB: Local version identifiers are NOT permitted in the version
+        # specifier, so local version labels can be universally removed from
+        # the prospective version.
+        return Version(prospective.public) <= Version(spec)
 
     @_require_version_compare
     def _compare_greater_than_equal(self, prospective, spec):
         # type: (ParsedVersion, str) -> bool
-        return prospective >= Version(spec)
+
+        # NB: Local version identifiers are NOT permitted in the version
+        # specifier, so local version labels can be universally removed from
+        # the prospective version.
+        return Version(prospective.public) >= Version(spec)
 
     @_require_version_compare
     def _compare_less_than(self, prospective, spec_str):
diff --git a/tests/test_specifiers.py b/tests/test_specifiers.py
index ee54dc84..6126f365 100644
--- a/tests/test_specifiers.py
+++ b/tests/test_specifiers.py
@@ -976,3 +976,17 @@ def test_comparison_canonicalizes(self, left, right):
     def test_comparison_non_specifier(self):
         assert SpecifierSet("==1.0") != 12
         assert not SpecifierSet("==1.0") == 12
+
+    @pytest.mark.parametrize(
+        ("version", "specifier", "expected"),
+        [
+            ("1.0.0+local", "==1.0.0", True),
+            ("1.0.0+local", "!=1.0.0", False),
+            ("1.0.0+local", "<=1.0.0", True),
+            ("1.0.0+local", ">=1.0.0", True),
+            ("1.0.0+local", "<1.0.0", False),
+            ("1.0.0+local", ">1.0.0", False),
+        ],
+    )
+    def test_comparison_ignores_local(self, version, specifier, expected):
+        assert (Version(version) in SpecifierSet(specifier)) == expected