diff --git a/contrib/test_decoding/expected/repack.out b/contrib/test_decoding/expected/repack.out
index ac5473137d1..0d229050146 100644
--- a/contrib/test_decoding/expected/repack.out
+++ b/contrib/test_decoding/expected/repack.out
@@ -111,6 +111,16 @@ REPACK (CONCURRENTLY) repack_conc_replident;
 ERROR:  cannot execute REPACK (CONCURRENTLY) on relation "repack_conc_replident"
 DETAIL:  This operation does not support deferrable primary keys.
 HINT:  Use ALTER TABLE ... REPLICA IDENTITY USING INDEX to designate another index as replica identity.
+-- Doesn't support tables whose replica identity indexes were dropped, even
+-- if a workable primary key is present.
+ALTER TABLE repack_conc_replident DROP CONSTRAINT repack_conc_replident_pkey,
+	ADD PRIMARY KEY (i);
+CREATE UNIQUE INDEX replidx ON repack_conc_replident (i);
+ALTER TABLE repack_conc_replident REPLICA IDENTITY USING INDEX replidx;
+DROP INDEX replidx;
+REPACK (CONCURRENTLY) repack_conc_replident;
+ERROR:  cannot execute REPACK (CONCURRENTLY) on relation "repack_conc_replident"
+DETAIL:  Relation "repack_conc_replident" has no identity index.
 -- clean up
 DROP TABLE repack_conc_replident, clstrpart;
 -- verify that the pgrepack plugin cannot be called directly
diff --git a/contrib/test_decoding/sql/repack.sql b/contrib/test_decoding/sql/repack.sql
index e995c72d28d..6e51aedb72d 100644
--- a/contrib/test_decoding/sql/repack.sql
+++ b/contrib/test_decoding/sql/repack.sql
@@ -83,6 +83,15 @@ REPACK (CONCURRENTLY) repack_conc_replident;
 ALTER TABLE repack_conc_replident ADD PRIMARY KEY (i) DEFERRABLE;
 REPACK (CONCURRENTLY) repack_conc_replident;
 
+-- Doesn't support tables whose replica identity indexes were dropped, even
+-- if a workable primary key is present.
+ALTER TABLE repack_conc_replident DROP CONSTRAINT repack_conc_replident_pkey,
+	ADD PRIMARY KEY (i);
+CREATE UNIQUE INDEX replidx ON repack_conc_replident (i);
+ALTER TABLE repack_conc_replident REPLICA IDENTITY USING INDEX replidx;
+DROP INDEX replidx;
+REPACK (CONCURRENTLY) repack_conc_replident;
+
 -- clean up
 DROP TABLE repack_conc_replident, clstrpart;
 
diff --git a/src/backend/commands/repack.c b/src/backend/commands/repack.c
index 1fa48f8fcc0..83168a4e6f3 100644
--- a/src/backend/commands/repack.c
+++ b/src/backend/commands/repack.c
@@ -971,13 +971,11 @@ check_concurrent_repack_requirements(Relation rel, Oid *ident_idx_p)
 						  "REPLICA IDENTITY NOTHING" : "REPLICA IDENTITY FULL"));
 
 	/*
-	 * Obtain the replica identity index -- either one that has been set
-	 * explicitly, or a non-deferrable primary key.  If none of these cases
-	 * apply, the table cannot be repacked concurrently.  It might be possible
-	 * to have repack work with a FULL replica identity; however that requires
-	 * more work and is not implemented yet.
+	 * Obtain the replica identity index to use.  If there isn't one, the
+	 * table cannot be repacked concurrently.  (Replica identity FULL is not
+	 * supported yet.)
 	 */
-	ident_idx = GetRelationIdentityOrPK(rel);
+	ident_idx = RelationGetReplicaIndex(rel);
 	if (!OidIsValid(ident_idx))
 	{
 		/* This special case warrants its own error message */
diff --git a/src/backend/utils/cache/relcache.c b/src/backend/utils/cache/relcache.c
index a8b106e36af..541f30f0972 100644
--- a/src/backend/utils/cache/relcache.c
+++ b/src/backend/utils/cache/relcache.c
@@ -5075,6 +5075,13 @@ RelationGetPrimaryKeyIndex(Relation relation, bool deferrable_ok)
 /*
  * RelationGetReplicaIndex -- get OID of the relation's replica identity index
  *
+ * If replica identity is DEFAULT, then return the OID of the primary key, if
+ * it's not deferrable; if replica identity is INDEX, return the OID of the
+ * index with indisreplident, if one exists.
+ *
+ * Note that a working PK is not returned if identity is INDEX!  This is
+ * surprising if the replica identity index is dropped.  FIXME someday.
+ *
  * Returns InvalidOid if there is no such index.
  */
 Oid