diff --git a/lark/parsers/lalr_interactive_parser.py b/lark/parsers/lalr_interactive_parser.py
index d5a2152f..fbf0d1f1 100644
--- a/lark/parsers/lalr_interactive_parser.py
+++ b/lark/parsers/lalr_interactive_parser.py
@@ -6,6 +6,7 @@
 
 from lark.exceptions import UnexpectedToken
 from lark.lexer import Token, LexerThread
+from .lalr_parser_state import ParserState
 
 ###{standalone
 
@@ -14,7 +15,7 @@ class InteractiveParser:
 
     For a simpler interface, see the ``on_error`` argument to ``Lark.parse()``.
     """
-    def __init__(self, parser, parser_state, lexer_thread: LexerThread):
+    def __init__(self, parser, parser_state: ParserState, lexer_thread: LexerThread):
         self.parser = parser
         self.parser_state = parser_state
         self.lexer_thread = lexer_thread
@@ -63,15 +64,15 @@ def __copy__(self):
 
         Calls to feed_token() won't affect the old instance, and vice-versa.
         """
+        return self.copy()
+
+    def copy(self, deepcopy_values=True):
         return type(self)(
             self.parser,
-            copy(self.parser_state),
+            self.parser_state.copy(deepcopy_values=deepcopy_values),
             copy(self.lexer_thread),
         )
 
-    def copy(self):
-        return copy(self)
-
     def __eq__(self, other):
         if not isinstance(other, InteractiveParser):
             return False
@@ -109,7 +110,7 @@ def accepts(self):
         conf_no_callbacks.callbacks = {}
         for t in self.choices():
             if t.isupper(): # is terminal?
-                new_cursor = copy(self)
+                new_cursor = self.copy(deepcopy_values=False)
                 new_cursor.parser_state.parse_conf = conf_no_callbacks
                 try:
                     new_cursor.feed_token(self.lexer_thread._Token(t, ''))
diff --git a/lark/parsers/lalr_parser_state.py b/lark/parsers/lalr_parser_state.py
index 35056976..273bc002 100644
--- a/lark/parsers/lalr_parser_state.py
+++ b/lark/parsers/lalr_parser_state.py
@@ -54,16 +54,16 @@ def __eq__(self, other) -> bool:
         return len(self.state_stack) == len(other.state_stack) and self.position == other.position
 
     def __copy__(self):
+        return self.copy()
+
+    def copy(self, deepcopy_values=True) -> 'ParserState[StateT]':
         return type(self)(
             self.parse_conf,
             self.lexer, # XXX copy
             copy(self.state_stack),
-            deepcopy(self.value_stack),
+            deepcopy(self.value_stack) if deepcopy_values else copy(self.value_stack),
         )
 
-    def copy(self) -> 'ParserState[StateT]':
-        return copy(self)
-
     def feed_token(self, token: Token, is_end=False) -> Any:
         state_stack = self.state_stack
         value_stack = self.value_stack