diff --git a/src/poetry/core/semver/helpers.py b/src/poetry/core/semver/helpers.py
index 0ce090d89..690bb17d9 100644
--- a/src/poetry/core/semver/helpers.py
+++ b/src/poetry/core/semver/helpers.py
@@ -77,10 +77,14 @@ def parse_single_constraint(constraint: str) -> VersionConstraint:
     m = TILDE_PEP440_CONSTRAINT.match(constraint)
     if m:
         version = Version.parse(m.group("version"))
-        if version.release.precision == 2:
+        precision = version.release.precision
+
+        if precision == 2:
             high = version.stable.next_major()
-        else:
+        elif precision == 3:
             high = version.stable.next_minor()
+        else:
+            high = version.stable.next_patch()
 
         return VersionRange(version, high, include_min=True)
 
@@ -97,12 +101,16 @@ def parse_single_constraint(constraint: str) -> VersionConstraint:
         op = m.group("op")
         major = int(m.group(2))
         minor = m.group(3)
+        patch = m.group(4)
 
-        if minor is not None:
-            version = Version.from_parts(major, int(minor), 0)
+        if patch is not None:
+            version = Version.from_parts(major, int(minor), int(patch))
             result: VersionConstraint = VersionRange(
-                version, version.next_minor(), include_min=True
+                version, version.next_patch(), include_min=True
             )
+        elif minor is not None:
+            version = Version.from_parts(major, int(minor), 0)
+            result = VersionRange(version, version.next_minor(), include_min=True)
         else:
             if major == 0:
                 result = VersionRange(max=Version.from_parts(1, 0, 0))
diff --git a/tests/semver/test_helpers.py b/tests/semver/test_helpers.py
index d53e9e57d..7e6eba771 100644
--- a/tests/semver/test_helpers.py
+++ b/tests/semver/test_helpers.py
@@ -66,6 +66,12 @@ def test_parse_constraint(input: str, constraint: Version | VersionRange) -> Non
                 Version.from_parts(20, 0, 0), Version.from_parts(21, 0, 0), True
             ),
         ),
+        (
+            "20.*.*.*",
+            VersionRange(
+                Version.from_parts(20, 0, 0), Version.from_parts(21, 0, 0), True
+            ),
+        ),
         (
             "2.0.*",
             VersionRange(
@@ -90,6 +96,24 @@ def test_parse_constraint(input: str, constraint: Version | VersionRange) -> Non
                 Version.from_parts(2, 2, 0), Version.from_parts(2, 3, 0), True
             ),
         ),
+        (
+            "2.2.3.*",
+            VersionRange(
+                Version.from_parts(2, 2, 3), Version.from_parts(2, 2, 4), True
+            ),
+        ),
+        (
+            "2.2.3.X",
+            VersionRange(
+                Version.from_parts(2, 2, 3), Version.from_parts(2, 2, 4), True
+            ),
+        ),
+        (
+            "2.*.X.x",
+            VersionRange(
+                Version.from_parts(2, 0, 0), Version.from_parts(3, 0, 0), True
+            ),
+        ),
         ("0.*", VersionRange(max=Version.from_parts(1, 0, 0))),
         ("0.*.*", VersionRange(max=Version.from_parts(1, 0, 0))),
         ("0.x", VersionRange(max=Version.from_parts(1, 0, 0))),
@@ -160,18 +184,27 @@ def test_parse_constraint_wildcard(input: str, constraint: VersionRange) -> None
                 Version.from_parts(3, 5, 0), Version.from_parts(3, 6, 0), True
             ),
         ),
+    ],
+)
+def test_parse_constraint_tilde(input: str, constraint: VersionRange) -> None:
+    assert parse_constraint(input) == constraint
+
+
+@pytest.mark.parametrize(
+    "input,constraint",
+    [
         (
             "~=3.5",
             VersionRange(
                 Version.from_parts(3, 5, 0), Version.from_parts(4, 0, 0), True
             ),
-        ),  # PEP 440
+        ),
         (
             "~=3.5.3",
             VersionRange(
                 Version.from_parts(3, 5, 3), Version.from_parts(3, 6, 0), True
             ),
-        ),  # PEP 440
+        ),
         (
             "~=3.5.3rc1",
             VersionRange(
@@ -179,10 +212,16 @@ def test_parse_constraint_wildcard(input: str, constraint: VersionRange) -> None
                 Version.from_parts(3, 6, 0),
                 True,
             ),
-        ),  # PEP 440
+        ),
+        (
+            "~=3.5.3.6",
+            VersionRange(
+                Version.from_parts(3, 5, 3, 6), Version.from_parts(3, 5, 4, 0), True
+            ),
+        ),
     ],
 )
-def test_parse_constraint_tilde(input: str, constraint: VersionRange) -> None:
+def test_parse_constraint_tilde_pep440(input: str, constraint: VersionRange) -> None:
     assert parse_constraint(input) == constraint