diff --git a/syncode/dfa_mask_store.py b/syncode/dfa_mask_store.py
index a51f815b..402d7855 100644
--- a/syncode/dfa_mask_store.py
+++ b/syncode/dfa_mask_store.py
@@ -453,6 +453,13 @@ def _lookup_next_tokens(self, dfa_states: Iterable[DFAState], r: ParseResult) ->
                                 overapprox_token_ids |= self._lookup_table.complete_case_lookup(dfa_state)
                             elif len(accept_sequence) == 2:
                                 overapprox_token_ids |= self._lookup_next_tokens_for_dfa_state(dfa_state, accept_sequence[1])
+                            elif len(accept_sequence) == 3:
+                                # This is useful in under-approximating `grammar_strict` mode as they help improve the precision of SynCode
+                                if self._mode == 'grammar_strict':
+                                    # If the DFA state is a final state we can jump to the start of next terminal
+                                    if self._dfas.is_final(dfa_state): 
+                                        ignore_init_state = self._dfas.initial(accept_sequence[1])
+                                        overapprox_token_ids |= self._lookup_next_tokens_for_dfa_state(ignore_init_state, accept_sequence[2])
                             else:
                                 raise ValueError(f"Invalid accept sequence: {accept_sequence}")
         return overapprox_token_ids
diff --git a/syncode/parse_result.py b/syncode/parse_result.py
index 26b1aeb3..830aca5e 100644
--- a/syncode/parse_result.py
+++ b/syncode/parse_result.py
@@ -62,8 +62,14 @@ def from_accept_terminals(cur_accept_terminals, next_accept_terminals, remainder
                     for t2 in next_accept_terminals:
                         accept_sequences.add(AcceptSequence([final_terminal, t2]))
                     if ignore_terminals is not None:
-                        for t2 in ignore_terminals:
-                            accept_sequences.add(AcceptSequence([final_terminal, t2]))
+                        for tignore in ignore_terminals:
+                            accept_sequences.add(AcceptSequence([final_terminal, tignore]))
+                        
+                        # These 3 length accept sequences are useful in under-approximating 
+                        # `grammar_strict` mode as they help improve the precision of SynCode
+                        for tignore in ignore_terminals:
+                            for t2 in next_accept_terminals:
+                                accept_sequences.add(AcceptSequence([final_terminal, tignore, t]))
                 else:
                     accept_sequences.add(AcceptSequence([t]))
         
diff --git a/tests/test_misc.py b/tests/test_misc.py
index 17a9f617..ab74a2ae 100644
--- a/tests/test_misc.py
+++ b/tests/test_misc.py
@@ -32,7 +32,35 @@ def test_mask_store_misc(self):
         dfa_mask = DFAMaskStore.load_dfa_mask_store(grammar=grammar, tokenizer=tokenizer, use_cache=False, logger=common.EmptyLogger())
         mask = dfa_mask.get_accept_mask(r, get_list=True)
         self.assertNotIn(' (', mask)
+    
+    @staticmethod
+    def essay_grammar():
+        # A Lark grammar for paragraphs in text
+        return """
+        start: paragraph+
+        ?paragraph: sentence+
+        ?sentence: word+ punctuation
+        word: /[a-zA-Z0-9]+/ | COMMA | SINGLE_QUOTE | ESCAPED_DOUBLE_QUOTE
+        punctuation: /[.!?]/
+        COMMA: ","
+        SINGLE_QUOTE: "'"
+        ESCAPED_DOUBLE_QUOTE: "\\\""
+
+        %import common.WS
+        %ignore WS
+    """
+
+    def test_mask_store_misc2(self):
+        grammar = Grammar(TestParserMisc.essay_grammar())
+        model = 'microsoft/Phi-3-mini-128k-instruct'
+        tokenizer = common.load_tokenizer(model)
+        inc_parser = create_parser(grammar)
+        r = inc_parser.get_acceptable_next_terminals("I")
+        dfa_mask = DFAMaskStore.load_dfa_mask_store(grammar=grammar, tokenizer=tokenizer, use_cache=False, logger=common.EmptyLogger())
+        mask = dfa_mask.get_accept_mask(r, get_list=True)
+        self.assertIn(' have', mask)
         
+
     def test_parser_calc(self):
         inc_parser = create_parser(Grammar('calc'))
         partial_code = "113 + 235 + 17"