diff --git a/scripts/slots.py b/scripts/slots.py
index 8e336db7..18c4ba49 100644
--- a/scripts/slots.py
+++ b/scripts/slots.py
@@ -355,14 +355,17 @@ def format_decision(decision: Decision) -> str:
     conflict = decision.conflict
     if decision.serves_both:
         winner = decision.winner.local_path
-        served = sorted({
-            c.emulator for c in conflict.profile_claims
-            if c.emulator and c.local_path == winner
-        })
-        others = sorted({
+        # A claim that only matched a path is answered by whatever file sits
+        # there; only one that pins content can be left wanting.
+        pinned_elsewhere = {
             c.emulator for c in conflict.profile_claims
             if c.emulator and c.local_path != winner
-        })
+            and resolution_is_hash_exact(c.status)
+        }
+        served = sorted({
+            c.emulator for c in conflict.profile_claims if c.emulator
+        } - pinned_elsewhere)
+        others = sorted(pinned_elsewhere)
         line = (
             f"{conflict.destination}: serve {winner} "
             f"({', '.join(served) or 'profile'}); the frontend only "
diff --git a/tests/test_slots.py b/tests/test_slots.py
index 11878bc2..752c28af 100644
--- a/tests/test_slots.py
+++ b/tests/test_slots.py
@@ -573,7 +573,22 @@ class StrongestProfileClaimWins(unittest.TestCase):
         )
         decision = arbitrate(conflict, "existence")
         self.assertEqual(decision.winner.emulator, "yaps2")
-        self.assertIn("armsx2 expected another file", format_decision(decision))
+        # armsx2 names no content: the file at the path answers it too.
+        line = format_decision(decision)
+        self.assertIn("(armsx2, yaps2)", line)
+        self.assertNotIn("expected another file", line)
+
+        pinned = Conflict(
+            conflict.destination,
+            conflict.platform_claim,
+            [claim("armsx2", "a", "md5_exact"), claim("yaps2", "y", "sha1_exact")],
+        )
+        # Both pin content: the tie goes to the first, the other is named.
+        self.assertIn(
+            "yaps2 expected another file",
+            format_decision(arbitrate(pinned, "existence")),
+        )
+
 
 if __name__ == "__main__":
     unittest.main()