diff --git a/tests/v1/core/test_async_scheduler.py b/tests/v1/core/test_async_scheduler.py
index 6d870b5640dfb..e0645ed43015e 100644
--- a/tests/v1/core/test_async_scheduler.py
+++ b/tests/v1/core/test_async_scheduler.py
@@ -34,15 +34,20 @@ def test_stop_by_max_tokens(max_tokens: int):
     requests = create_requests(num_requests=2, max_tokens=max_tokens)
     req0, req1 = requests
 
+    expected_total_num_scheduled_tokens = 0
     sched_outputs: deque[SchedulerOutput] = deque()
     scheduler.add_request(req0)
     sched_outputs.append(scheduler.schedule())
+    expected_total_num_scheduled_tokens += req0.num_prompt_tokens + max_tokens - 1
 
     scheduler.add_request(req1)
     sched_outputs.append(scheduler.schedule())
+    expected_total_num_scheduled_tokens += req1.num_prompt_tokens + max_tokens - 1
 
+    total_num_scheduled_tokens = 0
     while sched_outputs:
         sched_output = sched_outputs.popleft()
+        total_num_scheduled_tokens += sched_output.total_num_scheduled_tokens
         model_runner_output = _make_model_runner_output(sched_output)
         scheduler.update_from_output(sched_output, model_runner_output)
 
@@ -53,6 +58,8 @@ def test_stop_by_max_tokens(max_tokens: int):
     assert scheduler.get_num_unfinished_requests() == 0
     assert req0.num_output_tokens == max_tokens
     assert req1.num_output_tokens == max_tokens
+    # Ensure we aren't scheduling more tokens than necessary.
+    assert total_num_scheduled_tokens == expected_total_num_scheduled_tokens
 
 
 def test_abort():
diff --git a/tests/v1/e2e/test_spec_decode.py b/tests/v1/e2e/test_spec_decode.py
index 9b55d2b14b991..ffd9f3e0370f7 100644
--- a/tests/v1/e2e/test_spec_decode.py
+++ b/tests/v1/e2e/test_spec_decode.py
@@ -155,7 +155,6 @@ def test_suffix_decoding_acceptance(
     )
 
     # Run several times and check that the accepted tokens increase.
-    spec_llm.chat(test_prompts, sampling_config)
     num_draft = []
     num_accept = []
     for i in range(10):  # Run multiple times to warm up the cache.
diff --git a/vllm/v1/core/sched/scheduler.py b/vllm/v1/core/sched/scheduler.py
index aeb9869c52813..97341c762b99d 100644
--- a/vllm/v1/core/sched/scheduler.py
+++ b/vllm/v1/core/sched/scheduler.py
@@ -217,10 +217,14 @@ class Scheduler(SchedulerInterface):
                 num_new_tokens = self.scheduler_config.long_prefill_token_threshold
             num_new_tokens = min(num_new_tokens, token_budget)
 
-            # Make sure the input position does not exceed the max model len.
-            # This is necessary when using spec decoding.
+            # Make sure the input position does not exceed the max model len or
+            # request's max_tokens.
+            # This is necessary when using spec decoding and/or async scheduling.
+            max_total_tokens = min(
+                request.num_prompt_tokens + request.max_tokens, self.max_model_len
+            )
             num_new_tokens = min(
-                num_new_tokens, self.max_model_len - 1 - request.num_computed_tokens
+                num_new_tokens, max_total_tokens - 1 - request.num_computed_tokens
             )
 
             # Schedule encoder inputs.