diff --git a/src/univers/version_range.py b/src/univers/version_range.py
index c62d5b21..4a885f0d 100644
--- a/src/univers/version_range.py
+++ b/src/univers/version_range.py
@@ -664,11 +664,6 @@ class PypiVersionRange(VersionRange):
         ">=": ">=",
         "<": "<",
         ">": ">",
-        # per https://www.python.org/dev/peps/pep-0440/#compatible-release
-        # For a given release identifier V.N, the compatible release clause is
-        # approximately equivalent to the pair of comparison clauses:
-        # >= V.N, == V.*
-        "~=": None,
         # 01.01.01 is NOT equal to 1.1.1 using === which is strict string
         # equality this is a rare and eventually non-suggested approach
         "===": None,
@@ -681,7 +676,7 @@ def from_native(cls, string):
         Raise an a univers.versions.InvalidVersion
         """
         # TODO: environment markers are yet supported
-        # TODO: handle  .* version, ~= and === operators
+        # TODO: handle === operators
 
         if ";" in string:
             raise InvalidVersionRange(f"Unsupported PyPI environment marker: {string!r}")
@@ -694,6 +689,8 @@ def from_native(cls, string):
                 f"Unsupported character: {unsupported_chars!r} " f"in PyPI version: {string!r}"
             )
 
+        string = cls.sanitize_constraints(string)
+
         try:
             specifiers = SpecifierSet(string)
         except InvalidSpecifier as e:
@@ -707,14 +704,10 @@ def from_native(cls, string):
             operator = spec.operator
             version = spec.version
 
-            if operator == "~=" or operator == "===":
+            if operator == "===":
                 msg = f"Unsupported PyPI version constraint operator: {spec!r}"
                 unsupported_messages.append(msg)
 
-            if str(version).endswith(".*"):
-                msg = f"Unsupported PyPI version: {spec!r}"
-                unsupported_messages.append(msg)
-
             try:
                 version = cls.version_class(version)
                 comparator = cls.vers_by_native_comparators[operator]
@@ -729,6 +722,35 @@ def from_native(cls, string):
 
         return cls(constraints=constraints)
 
+    @classmethod
+    def sanitize_constraints(cls, string):
+        constraints = []
+        try:
+            specifiers = SpecifierSet(string)
+        except InvalidSpecifier as e:
+            raise InvalidVersionRange() from e
+        for spec in specifiers:
+            operator = spec.operator
+            version = spec.version
+            if "*" in version:
+                pos = version.find("*")
+                version = version[: pos - 1]
+                if "==" in operator:
+                    constraints.extend(
+                        [f">= {version}", f"< {version[:pos - 2]}{str(int(version[pos - 2]) + 1)}"]
+                    )
+                elif "!=" in operator:
+                    constraints.extend(
+                        [f"< {version}", f">= {version[:pos - 2]}{str(int(version[pos - 2]) + 1)}"]
+                    )
+            elif "~=" in operator:
+                parts = version.split(".")
+                parts[-2] = str(int(parts[-2]) + 1)
+                constraints.extend([f">= {version}", f"< {'.'.join(parts[:-1])}"])
+            else:
+                constraints.append(f"{operator} {version}")
+        return ", ".join(constraints)
+
 
 class MavenVersionRange(VersionRange):
     """
diff --git a/tests/test_version_range.py b/tests/test_version_range.py
index c92de0b7..4be2fb12 100644
--- a/tests/test_version_range.py
+++ b/tests/test_version_range.py
@@ -357,13 +357,14 @@ def test_from_native_and_from_string_round_trip(scheme, native_ranges):
 @pytest.mark.parametrize(
     "range, will_pass, expected",
     [
-        (" ~= 0.9", False, "Unsupported PyPI version constraint operator"),
-        ("~= 1.3", False, "Unsupported PyPI version constraint operator"),
+        (" ~= 0.9", True, "vers:pypi/>=0.9|<1"),
+        ("~= 1.3", True, "vers:pypi/>=1.3|<2"),
         (" >= 1.0", True, "vers:pypi/>=1.0"),
-        (" != 1.3.4.*", False, "Unsupported PyPI version"),
+        (" != 1.3.4.*", True, "vers:pypi/<1.3.4|>=1.3.5"),
         ("< 2.0", True, "vers:pypi/<2.0"),
         ("~= 1.3.4.*", False, ""),
-        ("==1. *", False, "Unsupported PyPI version"),
+        ("==1. *", True, "vers:pypi/>=1|<2"),
+        ("!=1.2.*", True, "vers:pypi/<1.2|>=1.3"),
         ("==1.3.4 ) (", False, "Unsupported character"),
         ("===1.0", False, "Unsupported PyPI version"),
     ],
@@ -375,6 +376,7 @@ def test_PypiVersionRange_raises_ivr_for_unsupported_and_invalid_ranges(range, w
             raise Exception("Exception not raised")
         except InvalidVersionRange as ivre:
             assert expected in str(ivre)
+
     else:
         assert expected == str(PypiVersionRange.from_native(range))