diff --git a/opt_prime/opt_prime/accel/pd/paged.py b/opt_prime/opt_prime/accel/pd/paged.py
index d9e5f0df..a9b0bf5c 100644
--- a/opt_prime/opt_prime/accel/pd/paged.py
+++ b/opt_prime/opt_prime/accel/pd/paged.py
@@ -166,6 +166,8 @@ def __init__(self, layers, slots, kv_heads, head_dim, dtype, device, *, pages, p
         """groups: `torch_models.KVGroup`s of a hybrid model; default one full-attention group of all layers"""
         if max_context % page_size:
             raise ValueError("max_context must be a multiple of page_size")
+        if pages < max_context // page_size:                     # else a max_context request is never admitted
+            raise ValueError("pages must hold one max_context request")
         self.page_size, self.pages, self.slots = page_size, pages, slots
         if groups is None:
             from opt_prime.accel.pd.torch_models import KVGroup
diff --git a/opt_prime/tests/test_pd_batching.py b/opt_prime/tests/test_pd_batching.py
index 047c77d3..fbe99925 100644
--- a/opt_prime/tests/test_pd_batching.py
+++ b/opt_prime/tests/test_pd_batching.py
@@ -133,7 +133,7 @@ def test_moe_family_and_rejections(kv):
 def test_paged_admission_follows_pages_not_slots():
     """with paged KV a request takes only the pages it needs; admission waits for pages, not for max_context"""
     model = _llama()
-    b = ContinuousBatcher(model, kv="paged", slots=8, max_context=128, prefill_chunk=64, page_size=16, pages=6)
+    b = ContinuousBatcher(model, kv="paged", slots=8, max_context=96, prefill_chunk=64, page_size=16, pages=6)
     prompts = _prompts(5, 10, 30, seed=2)
     fs = [b.submit(PDRequest(f"p{i}", p, 8)) for i, p in enumerate(prompts)]     # each needs 2-3 pages
     b.step()
@@ -142,3 +142,9 @@ def test_paged_admission_follows_pages_not_slots():
     for p, f in zip(prompts, fs):
         assert f.result() == _greedy(model, p, 8)
     assert len(b.kv.free_pages) == 6 and all(not o for o in b.kv.owned)
+
+
+def test_paged_pool_smaller_than_one_request_is_rejected():
+    """#169: a request admitted by max_context must fit the pool, or it blocks the FIFO queue forever"""
+    with pytest.raises(ValueError):
+        ContinuousBatcher(_llama(), kv="paged", slots=2, max_context=64, page_size=16, pages=2)