diff --git a/docs/changelog/159.bugfix.rst b/docs/changelog/159.bugfix.rst
new file mode 100644
index 0000000..3bf9421
--- /dev/null
+++ b/docs/changelog/159.bugfix.rst
@@ -0,0 +1,2 @@
+Match ``~=X.Y`` compatible-release specifiers against later minor versions, as PEP 440 defines, instead of only
+the same minor; ``~=3.10`` now accepts 3.11 and newer 3.x.
diff --git a/src/python_discovery/_specifier.py b/src/python_discovery/_specifier.py
index 2607631..f9f05ea 100644
--- a/src/python_discovery/_specifier.py
+++ b/src/python_discovery/_specifier.py
@@ -227,12 +227,10 @@ def _check_compatible_release(self, candidate: SimpleVersion) -> bool:
             return False
         if candidate < self.version:
             return False
-        if len(self.version.release) >= 2:  # ruff:ignore[magic-value-comparison]  # pragma: no branch # SimpleVersion always has 3-part release
-            upper_parts = list(self.version.release[:-1])
-            upper_parts[-1] += 1
-            upper = SimpleVersion.from_string(".".join(str(p) for p in upper_parts))
-            return candidate < upper
-        return True  # pragma: no cover
+        # ~=X.Y is >=X.Y, ==X.*: compare all but the last part the spec wrote (release is padded to three).
+        # A bare ~=X still compares its one part, so it stays ==X.*.
+        prefix = max(self.version_str.count("."), 1)
+        return candidate.release[:prefix] == self.version.release[:prefix]
 
     def __eq__(self, other: object) -> bool:
         if not isinstance(other, SimpleSpecifier):
diff --git a/tests/test_iter_interpreters.py b/tests/test_iter_interpreters.py
index c348b71..3452f92 100644
--- a/tests/test_iter_interpreters.py
+++ b/tests/test_iter_interpreters.py
@@ -297,6 +297,19 @@ def test_iter_interpreters_uv_layout(
             ["cpython-3.12.13-macos-aarch64-none/bin/python"],
             id="specifier-rules-out-the-rest",
         ),
+        pytest.param(
+            (
+                "cpython-3.9.25-macos-aarch64-none/bin/python",
+                "cpython-3.10.19-macos-aarch64-none/bin/python",
+                "cpython-3.13.7-macos-aarch64-none/bin/python",
+            ),
+            "~=3.10",
+            [
+                "cpython-3.13.7-macos-aarch64-none/bin/python",
+                "cpython-3.10.19-macos-aarch64-none/bin/python",
+            ],
+            id="compatible-release-keeps-later-minors",
+        ),
         pytest.param(
             (
                 "cpython-3.14.6-macos-aarch64-none/bin/python",
diff --git a/tests/test_py_info_extra.py b/tests/test_py_info_extra.py
index 4995b86..b2e5bd4 100644
--- a/tests/test_py_info_extra.py
+++ b/tests/test_py_info_extra.py
@@ -211,6 +211,9 @@ def test_satisfies_version_specifier_fails() -> None:
         pytest.param(VersionInfo(3, 15, 0, "final", 0), "<3.15.0a6", False, id="final_not_less_than_prerelease"),
         pytest.param(VersionInfo(3, 15, 0, "final", 0), ">=3.15", True, id="final_match_major_minor"),
         pytest.param(VersionInfo(3, 15, 1, "alpha", 1), ">=3.15.0", True, id="later_micro_prerelease_match"),
+        pytest.param(VersionInfo(3, 13, 7, "final", 0), "~=3.10", True, id="compatible_release_later_minor"),
+        pytest.param(VersionInfo(4, 0, 0, "final", 0), "~=3.10", False, id="compatible_release_next_major"),
+        pytest.param(VersionInfo(3, 13, 0, "alpha", 1), "~=3.12.0", False, id="compatible_release_next_minor_alpha"),
     ],
 )
 def test_satisfies_version_specifier_prerelease(version_info: VersionInfo, spec_str: str, expected: bool) -> None:
diff --git a/tests/test_specifier.py b/tests/test_specifier.py
index 6091452..2c3d218 100644
--- a/tests/test_specifier.py
+++ b/tests/test_specifier.py
@@ -149,6 +149,12 @@ def test_specifier_parse_wildcard() -> None:
         pytest.param("~=3.12.0", "3.13.0", False, id="compatible-next-minor"),
         pytest.param("~=3.12.0", "3.11.0", False, id="compatible-below"),
         pytest.param("~=3.12.0", "3.11.9", False, id="compatible-just-below"),
+        pytest.param("~=3.12.0", "3.13.0a1", False, id="compatible-next-minor-prerelease"),
+        pytest.param("~=3.10", "3.13.7", True, id="compatible-two-part-next-minor"),
+        pytest.param("~=3.10", "3.9.25", False, id="compatible-two-part-below"),
+        pytest.param("~=3.10", "4.0.0", False, id="compatible-two-part-next-major"),
+        pytest.param("~=3.10", "4.0.0a1", False, id="compatible-two-part-next-major-prerelease"),
+        pytest.param("~=3.13rc1", "3.14.0", True, id="compatible-two-part-prerelease-next-minor"),
         pytest.param(">=3.12", "not_a_version", False, id="invalid-version"),
     ],
 )
@@ -297,3 +303,5 @@ def test_specifier_compatible_release_major_only() -> None:
     spec = SimpleSpecifier.from_string("~=3")
     assert spec.contains("3.0.0") is True
     assert spec.contains("3.0.5") is True
+    assert spec.contains("3.13.7") is True
+    assert spec.contains("4.0.0") is False