diff --git a/backend/tests/accounts/test_db_engines.py b/backend/tests/accounts/test_db_engines.py
index 29454d5..cbe6e24 100644
--- a/backend/tests/accounts/test_db_engines.py
+++ b/backend/tests/accounts/test_db_engines.py
@@ -9,6 +9,28 @@ from sqlalchemy import select
 
 from accounts import db
 
+# The server-side ceiling these pools spend from, and the deployment shape that
+# spends it. Kept here so a pool change that stops fitting is a failing test
+# rather than a 2am "sorry, too many clients already". Mirrors max_connections in
+# infra/deploy/db/init/20-tuning.sh. ONE Postgres instance serves prod and beta.
+MAX_CONNECTIONS = 200
+PROD_WEB_WORKERS = 4           # uvicorn workers per prod web replica
+BETA_WEB_WORKERS = 2
+ASYNC_ENGINES_PER_PROCESS = 2  # RW + RO, both built from _ASYNC_POOL_KWARGS
+
+
+def _async_ceiling_per_process() -> int:
+    """Connections one backend process can hold from its async pools at once."""
+    k = db._ASYNC_POOL_KWARGS
+    return ASYNC_ENGINES_PER_PROCESS * (k["pool_size"] + k["max_overflow"])
+
+
+def _sync_ceiling() -> int:
+    """The notifier's sync pool. One process holds it cluster-wide (leader flock),
+    so it is NOT multiplied by workers or replicas."""
+    k = db._SYNC_POOL_KWARGS
+    return k["pool_size"] + k["max_overflow"]
+
 
 def test_defaults_to_sqlite_when_no_database_url():
     assert db.IS_POSTGRES is False
@@ -32,13 +54,18 @@ def test_postgres_pool_sizing_and_sync_timeouts():
     """The Postgres engine-construction kwargs, defined at module scope so they're
     testable without a real Postgres connection (the engines built from them are
     only actually constructed when IS_POSTGRES, exercised by the docker-compose
-    stack -- see the module docstring). pool_size=1/max_overflow=1 (the old
+    stack -- see the module docstring). pool_size=1/max_overflow=1 (the original
     setting) let a 3rd concurrent request per worker wait out pool_timeout for a
-    slot; both async engines need real headroom, and the sync engine (the
+    slot, so the steady-state pool needs real headroom; the sync engine (the
     notifier's, driven off-event-loop) must bound connect + statement time so a
     wedged Postgres can't hang it forever under its leader flock."""
     assert db._ASYNC_POOL_KWARGS["pool_size"] >= 5
-    assert db._ASYNC_POOL_KWARGS["max_overflow"] >= 5
+
+    # The overflow is the part nobody budgets for -- it is multiplied by two async
+    # engines x uvicorn workers x replicas, against a ceiling shared with beta.
+    # Prod saturated max_connections on 2026-07-26 with this at 5. Keep it well
+    # under pool_size; the budget test below is the real constraint.
+    assert db._ASYNC_POOL_KWARGS["max_overflow"] <= 2
 
     assert db._SYNC_POOL_KWARGS["pool_size"] < db._ASYNC_POOL_KWARGS["pool_size"]
     connect_args = db._SYNC_POOL_KWARGS["connect_args"]
@@ -53,6 +80,27 @@ def test_postgres_pool_sizing_and_sync_timeouts():
     engine.dispose()
 
 
+def test_pool_budget_fits_under_max_connections():
+    """At today's replica counts the whole estate's configured worst case must fit
+    inside the server's max_connections, with margin -- prod web + prod worker +
+    beta web + beta worker all draw on ONE Postgres instance. This is the test
+    that would have failed before 2026-07-26, when the configured worst case was
+    170 against a ceiling of 100.
+
+    Note this counts *configured maxima*: every pool at full overflow at the same
+    instant. Prod web autoscaling to its max of 3 replicas is deliberately NOT in
+    this sum -- that peak still does not fit, and closing it needs a connection
+    pooler or a lower autoscale ceiling rather than a bigger number here."""
+    per_process = _async_ceiling_per_process()
+    prod = per_process * PROD_WEB_WORKERS + (per_process + _sync_ceiling())
+    beta = per_process * BETA_WEB_WORKERS + (per_process + _sync_ceiling())
+
+    assert prod + beta <= MAX_CONNECTIONS * 0.8, (
+        f"configured worst case {prod + beta} leaves too little room under "
+        f"max_connections={MAX_CONNECTIONS}"
+    )
+
+
 def test_read_session_yields_a_working_session():
     # On SQLite the read session is fully usable (no read-only enforcement); this
     # just confirms the dependency wiring resolves to a live AsyncSession.