diff --git a/jax/experimental/key_reuse/_forwarding.py b/jax/experimental/key_reuse/_forwarding.py
index db5a9dc9359f..3e46c8b12ab8 100644
--- a/jax/experimental/key_reuse/_forwarding.py
+++ b/jax/experimental/key_reuse/_forwarding.py
@@ -260,16 +260,20 @@ def _scan_key_type_signature(eqn, args_consumed):
 
   # scan body should not consume key in constants
   if any(np.any(s.mask) for s in signature.sinks if s.idx < num_consts):
-    raise KeyReuseError("scan body function leads to key reuse when repeatedly executed:\n"
+    raise KeyReuseError("scan body function leads to key reuse when repeatedly executed, "
+                        "because key constants are repeatedly consumed:\n"
                         f"  {signature=}\n"
                         f"  {eqn=}\n"
                         f"  {jaxpr=}")
 
   # scan carry should only consume keys that are sourced on output.
-  carry_sinks = {s.idx - num_consts: s.mask for s in signature.sinks if 0 <= s.idx - num_consts < num_carry}
-  carry_sources = {s.idx: s.mask for s in signature.sources if 0 <= s.idx < num_carry}
-  if carry_sinks.keys() != carry_sources.keys():  # TODO(jakevdp): check that masks match
-    raise KeyReuseError(f"scan body function leads to key reuse when repeatedly executed:\n"
+  carry_sinks = {s.idx - num_consts: s.mask for s in signature.sinks
+                 if 0 <= s.idx - num_consts < num_carry and np.any(s.mask)}
+  carry_sources = {s.idx: s.mask for s in signature.sources
+                   if 0 <= s.idx < num_carry and np.any(s.mask)}
+  if not set(carry_sinks).issubset(set(carry_sources)):  # TODO(jakevdp): check that masks match
+    raise KeyReuseError("scan body function leads to key reuse when repeatedly executed, "
+                        "because consumed inputs don't match sourced outputs:\n"
                         f"  {signature=}\n"
                         f"  {eqn=}\n"
                         f"  {jaxpr=}")
diff --git a/jax/experimental/key_reuse/_simple.py b/jax/experimental/key_reuse/_simple.py
index edc4f2a460db..0d379587cf65 100644
--- a/jax/experimental/key_reuse/_simple.py
+++ b/jax/experimental/key_reuse/_simple.py
@@ -231,16 +231,20 @@ def _scan_key_type_signature(eqn, args_consumed):
 
   # scan body should not consume key in constants
   if any(np.any(s.mask) for s in signature.sinks if s.idx < num_consts):
-    raise KeyReuseError(f"scan body function leads to key reuse when repeatedly executed:\n"
+    raise KeyReuseError("scan body function leads to key reuse when repeatedly executed, "
+                        "because key constants are repeatedly consumed:\n"
                         f"  {signature=}\n"
                         f"  {eqn=}\n"
                         f"  {jaxpr=}")
 
   # scan carry should only consume keys that are sourced on output.
-  carry_sinks = {s.idx - num_consts: s.mask for s in signature.sinks if 0 <= s.idx - num_consts < num_carry}
-  carry_sources = {s.idx: s.mask for s in signature.sources if 0 <= s.idx < num_carry}
-  if carry_sinks.keys() != carry_sources.keys():  # TODO(jakevdp): check that masks match
-    raise KeyReuseError(f"scan body function leads to key reuse when repeatedly executed:\n"
+  carry_sinks = {s.idx - num_consts: s.mask for s in signature.sinks
+                 if 0 <= s.idx - num_consts < num_carry and np.any(s.mask)}
+  carry_sources = {s.idx: s.mask for s in signature.sources
+                   if 0 <= s.idx < num_carry and np.any(s.mask)}
+  if not set(carry_sinks).issubset(set(carry_sources)):
+    raise KeyReuseError("scan body function leads to key reuse when repeatedly executed, "
+                        "because consumed inputs don't match sourced outputs:\n"
                         f"  {signature=}\n"
                         f"  {eqn=}\n"
                         f"  {jaxpr=}")
diff --git a/tests/key_reuse_test.py b/tests/key_reuse_test.py
index 5ebecf4d4e19..0cda84d99b78 100644
--- a/tests/key_reuse_test.py
+++ b/tests/key_reuse_test.py
@@ -710,6 +710,13 @@ def f_scan_over_keys(key):
       return jax.lax.map(jax.random.bits, keys)
     self.check_key_reuse(f_scan_over_keys, jax.random.key(0))
 
+  def test_scan_consume_one(self):
+    def f_scan_over_keys(*keys):
+      def body_func(keys, x):
+        return tuple(jax.random.split(keys[0])), x
+      return jax.lax.scan(body_func, keys, xs=jnp.arange(10))
+    self.check_key_reuse(f_scan_over_keys, jax.random.key(0), jax.random.key(1))
+
   def test_vmap(self):
     @jax.vmap
     def f_good(seed):