diff --git a/rich/segment.py b/rich/segment.py
index 26ee041d..3222f3d2 100644
--- a/rich/segment.py
+++ b/rich/segment.py
@@ -312,7 +312,7 @@ class Segment(NamedTuple):
                 yield segment
             else:
                 text, style, _is_control = segment
-                yield cls(text, style.copy(link=None) if style else None)
+                yield cls(text, style.update_link(None) if style else None)
 
     @classmethod
     def strip_styles(cls, segments: Iterable["Segment"]) -> Iterable["Segment"]:
diff --git a/rich/style.py b/rich/style.py
index 707324a9..4eca6361 100644
--- a/rich/style.py
+++ b/rich/style.py
@@ -501,7 +501,7 @@ class Style:
         iter_styles = iter(styles)
         return sum(iter_styles, next(iter_styles))
 
-    def copy(self, link: str = None) -> "Style":
+    def copy(self) -> "Style":
         """Get a copy of this style.
 
         Returns:
@@ -516,9 +516,30 @@ class Style:
         style._bgcolor = self._bgcolor
         style._attributes = self._attributes
         style._set_attributes = self._set_attributes
-        _link = self._link if link is None else link
-        style._link = _link
-        style._link_id = f"{time()}-{randint(0, 999999)}" if _link else ""
+        style._link = self._link
+        style._link_id = f"{time()}-{randint(0, 999999)}" if self._link else ""
+        style._hash = self._hash
+        style._null = False
+        return style
+
+    def update_link(self, link: str = None) -> "Style":
+        """Get a copy with a different value for link.
+
+        Args:
+            link (str, optional): New value for link. Defaults to None.
+
+        Returns:
+            Style: A new Style instance.
+        """
+        style = self.__new__(Style)
+        style._ansi = self._ansi
+        style._style_definition = self._style_definition
+        style._color = self._color
+        style._bgcolor = self._bgcolor
+        style._attributes = self._attributes
+        style._set_attributes = self._set_attributes
+        style._link = link
+        style._link_id = f"{time()}-{randint(0, 999999)}" if link else ""
         style._hash = self._hash
         style._null = False
         return style
diff --git a/tests/test_segment.py b/tests/test_segment.py
index c5e24995..04e01ad8 100644
--- a/tests/test_segment.py
+++ b/tests/test_segment.py
@@ -86,3 +86,13 @@ def test_filter_control():
     assert list(Segment.filter_control(segments, is_control=True)) == [
         Segment("bar", is_control=True)
     ]
+
+
+def test_strip_styles():
+    segments = [Segment("foo", Style(bold=True))]
+    assert list(Segment.strip_styles(segments)) == [Segment("foo", None)]
+
+
+def test_strip_links():
+    segments = [Segment("foo", Style(bold=True, link="https://www.example.org"))]
+    assert list(Segment.strip_links(segments)) == [Segment("foo", Style(bold=True))]
\ No newline at end of file