diff --git a/tests/test_specifiers.py b/tests/test_specifiers.py
index ab343083..28f67796 100644
--- a/tests/test_specifiers.py
+++ b/tests/test_specifiers.py
@@ -576,6 +576,11 @@ def test_specifiers_prereleases(self, specifier, version, expected):
             # Test overriding with the overall specifier
             (">=1.0.dev1", True, None, ["1.0", "2.0a1"], ["1.0", "2.0a1"]),
             (">=1.0.dev1", False, None, ["1.0", "2.0a1"], ["1.0"]),
+            # Test when both specifier and filter have prerelease value
+            (">=1.0", True, False, ["1.0", "2.0a1"], ["1.0"]),
+            (">=1.0", False, True, ["1.0", "2.0a1"], ["1.0", "2.0a1"]),
+            (">=1.0", True, True, ["1.0", "2.0a1"], ["1.0", "2.0a1"]),
+            (">=1.0", False, False, ["1.0", "2.0a1"], ["1.0"]),
         ],
     )
     def test_specifier_filter(
@@ -749,6 +754,26 @@ def test_specifier_contains_installed_prereleases(self):
             (">=1.0.dev1", False, None, ["1.0", "2.0a1"], ["1.0"]),
             ("", True, None, ["1.0a1"], ["1.0a1"]),
             ("", False, None, ["1.0a1"], []),
+            # Test when both specifier and filter have prerelease value
+            (">=1.0", True, False, ["1.0", "2.0a1"], ["1.0"]),
+            (">=1.0", False, True, ["1.0", "2.0a1"], ["1.0", "2.0a1"]),
+            (">=1.0", True, True, ["1.0", "2.0a1"], ["1.0", "2.0a1"]),
+            (">=1.0", False, False, ["1.0", "2.0a1"], ["1.0"]),
+            # Test when there are multiple specifiers
+            (">=1.0,<=2.0", None, None, ["1.0", "1.5a1"], ["1.0"]),
+            (">=1.0,<=2.0dev", None, None, ["1.0", "1.5a1"], ["1.0", "1.5a1"]),
+            (">=1.0,<=2.0", True, None, ["1.0", "1.5a1"], ["1.0", "1.5a1"]),
+            (">=1.0,<=2.0", False, None, ["1.0", "1.5a1"], ["1.0"]),
+            (">=1.0,<=2.0dev", False, None, ["1.0", "1.5a1"], ["1.0"]),
+            (">=1.0,<=2.0dev", True, None, ["1.0", "1.5a1"], ["1.0", "1.5a1"]),
+            (">=1.0,<=2.0", None, False, ["1.0", "1.5a1"], ["1.0"]),
+            (">=1.0,<=2.0", None, True, ["1.0", "1.5a1"], ["1.0", "1.5a1"]),
+            (">=1.0,<=2.0dev", None, False, ["1.0", "1.5a1"], ["1.0"]),
+            (">=1.0,<=2.0dev", None, True, ["1.0", "1.5a1"], ["1.0", "1.5a1"]),
+            (">=1.0,<=2.0", True, False, ["1.0", "1.5a1"], ["1.0"]),
+            (">=1.0,<=2.0", False, True, ["1.0", "1.5a1"], ["1.0", "1.5a1"]),
+            (">=1.0,<=2.0dev", True, False, ["1.0", "1.5a1"], ["1.0"]),
+            (">=1.0,<=2.0dev", False, True, ["1.0", "1.5a1"], ["1.0", "1.5a1"]),
         ],
     )
     def test_specifier_filter(
diff --git a/tests/test_specifierset.py b/tests/test_specifierset.py
new file mode 100644
index 00000000..6d918eaf
--- /dev/null
+++ b/tests/test_specifierset.py
@@ -0,0 +1,47 @@
+import pytest
+
+from packaging.specifiers import SpecifierSet
+from packaging.version import Version
+
+
+class TestSpeicifierSet:
+    @pytest.mark.parametrize(
+        ("specifier", "specifier_prereleases", "prereleases", "input", "expected"),
+        [
+            # General test of the filter method
+            ("", None, None, ["1.0", "2.0a1"], ["1.0"]),
+            (">=1.0.dev1", None, None, ["1.0", "2.0a1"], ["1.0", "2.0a1"]),
+            ("", None, None, ["1.0a1"], ["1.0a1"]),
+            (">=1.2.3", None, None, ["1.2", "1.5a1"], ["1.5a1"]),
+            (">=1.2.3", None, None, ["1.3", "1.5a1"], ["1.3"]),
+            ("", None, None, ["1.0", Version("2.0")], ["1.0", Version("2.0")]),
+            (">=1.0", None, None, ["2.0a1"], ["2.0a1"]),
+            ("!=2.0a1", None, None, ["1.0a2", "1.0", "2.0a1"], ["1.0"]),
+            ("==2.0a1", None, None, ["2.0a1"], ["2.0a1"]),
+            (">2.0a1", None, None, ["2.0a1", "3.0a2", "3.0"], ["3.0a2", "3.0"]),
+            ("<2.0a1", None, None, ["1.0a2", "1.0", "2.0a1"], ["1.0a2", "1.0"]),
+            ("~=2.0a1", None, None, ["1.0", "2.0a1", "3.0a2", "3.0"], ["2.0a1"]),
+            # Test overriding with the prereleases parameter on filter
+            ("", None, False, ["1.0a1"], []),
+            (">=1.0.dev1", None, False, ["1.0", "2.0a1"], ["1.0"]),
+            ("", None, True, ["1.0", "2.0a1"], ["1.0", "2.0a1"]),
+            # Test overriding with the overall specifier
+            ("", True, None, ["1.0", "2.0a1"], ["1.0", "2.0a1"]),
+            ("", False, None, ["1.0", "2.0a1"], ["1.0"]),
+            (">=1.0.dev1", True, None, ["1.0", "2.0a1"], ["1.0", "2.0a1"]),
+            (">=1.0.dev1", False, None, ["1.0", "2.0a1"], ["1.0"]),
+            ("", True, None, ["1.0a1"], ["1.0a1"]),
+            ("", False, None, ["1.0a1"], []),
+        ],
+    )
+    def test_specifier_filter(
+        self, specifier_prereleases, specifier, prereleases, input, expected
+    ):
+        if specifier_prereleases is None:
+            spec = SpecifierSet(specifier)
+        else:
+            spec = SpecifierSet(specifier, prereleases=specifier_prereleases)
+
+        kwargs = {"prereleases": prereleases} if prereleases is not None else {}
+
+        assert list(spec.filter(input, **kwargs)) == expected