diff --git a/sqlparse/filters/others.py b/sqlparse/filters/others.py
index 95bc436c..109d44c2 100644
--- a/sqlparse/filters/others.py
+++ b/sqlparse/filters/others.py
@@ -112,11 +112,16 @@ def _stripws_identifierlist(self, tlist):
         return self._stripws_default(tlist)
 
     def _stripws_parenthesis(self, tlist):
-        while tlist.tokens[1].is_whitespace:
+        # A well-formed parenthesis has an opening and closing token plus the
+        # content in between, so tokens[1]/tokens[-2] address the inner edges.
+        # Degenerate groups can hold fewer tokens (e.g. "(::)" is grouped as a
+        # single Identifier), leaving nothing to strip; guard against indexing
+        # past the ends in that case.
+        while len(tlist.tokens) > 2 and tlist.tokens[1].is_whitespace:
             tlist.tokens.pop(1)
-        while tlist.tokens[-2].is_whitespace:
+        while len(tlist.tokens) > 2 and tlist.tokens[-2].is_whitespace:
             tlist.tokens.pop(-2)
-        if tlist.tokens[-2].is_group:
+        if len(tlist.tokens) > 2 and tlist.tokens[-2].is_group:
             # save to remove the last whitespace
             while tlist.tokens[-2].tokens[-1].is_whitespace:
                 tlist.tokens[-2].tokens.pop(-1)
diff --git a/tests/test_format.py b/tests/test_format.py
index 0cdbcf88..52e57df0 100644
--- a/tests/test_format.py
+++ b/tests/test_format.py
@@ -784,3 +784,14 @@ def test_strip_ws_removes_trailing_ws_in_groups():  # issue782
                                 strip_whitespace=True)
     expected = '(where foo = bar) from'
     assert formatted == expected
+
+
+def test_strip_ws_degenerate_parenthesis_group():
+    # "(::)" is grouped as a single Identifier, so the enclosing Parenthesis
+    # holds too few tokens for the whitespace stripper to index its inner
+    # edges. Formatting must not raise IndexError.
+    assert sqlparse.format('(::)', strip_whitespace=True) == '(::)'
+    assert sqlparse.format('( :: )', reindent=True) == '( :: )'
+    assert sqlparse.format('count(::)', strip_whitespace=True) == 'count(::)'
+    # Normal parentheses still have their inner whitespace stripped.
+    assert sqlparse.format('( a )', strip_whitespace=True) == '(a)'