diff --git a/src/backend/catalog/index.c b/src/backend/catalog/index.c
index e6579f2979..41b16cb89b 100644
--- a/src/backend/catalog/index.c
+++ b/src/backend/catalog/index.c
@@ -3482,9 +3482,8 @@ index_set_state_flags(Oid indexId, IndexStateFlagsAction action)
 			 * CONCURRENTLY that failed partway through.)
 			 *
 			 * Note: the CLUSTER logic assumes that indisclustered cannot be
-			 * set on any invalid index, so clear that flag too.  Similarly,
-			 * ALTER TABLE assumes that indisreplident cannot be set for
-			 * invalid indexes.
+			 * set on any invalid index, so clear that flag too.  For
+			 * cleanliness, also clear indisreplident.
 			 */
 			indexForm->indisvalid = false;
 			indexForm->indisclustered = false;
diff --git a/src/backend/commands/tablecmds.c b/src/backend/commands/tablecmds.c
index 7c697a285b..1293545947 100644
--- a/src/backend/commands/tablecmds.c
+++ b/src/backend/commands/tablecmds.c
@@ -15773,7 +15773,10 @@ ATExecDropOf(Relation rel, LOCKMODE lockmode)
  * relation_mark_replica_identity: Update a table's replica identity
  *
  * Iff ri_type = REPLICA_IDENTITY_INDEX, indexOid must be the Oid of a suitable
- * index. Otherwise, it should be InvalidOid.
+ * index. Otherwise, it must be InvalidOid.
+ *
+ * Caller had better hold an exclusive lock on the relation, as the results
+ * of running two of these concurrently wouldn't be pretty.
  */
 static void
 relation_mark_replica_identity(Relation rel, char ri_type, Oid indexOid,
@@ -15785,7 +15788,6 @@ relation_mark_replica_identity(Relation rel, char ri_type, Oid indexOid,
 	HeapTuple	pg_index_tuple;
 	Form_pg_class pg_class_form;
 	Form_pg_index pg_index_form;
-
 	ListCell   *index;
 
 	/*
@@ -15807,29 +15809,7 @@ relation_mark_replica_identity(Relation rel, char ri_type, Oid indexOid,
 	heap_freetuple(pg_class_tuple);
 
 	/*
-	 * Check whether the correct index is marked indisreplident; if so, we're
-	 * done.
-	 */
-	if (OidIsValid(indexOid))
-	{
-		Assert(ri_type == REPLICA_IDENTITY_INDEX);
-
-		pg_index_tuple = SearchSysCache1(INDEXRELID, ObjectIdGetDatum(indexOid));
-		if (!HeapTupleIsValid(pg_index_tuple))
-			elog(ERROR, "cache lookup failed for index %u", indexOid);
-		pg_index_form = (Form_pg_index) GETSTRUCT(pg_index_tuple);
-
-		if (pg_index_form->indisreplident)
-		{
-			ReleaseSysCache(pg_index_tuple);
-			return;
-		}
-		ReleaseSysCache(pg_index_tuple);
-	}
-
-	/*
-	 * Clear the indisreplident flag from any index that had it previously,
-	 * and set it for any index that should have it now.
+	 * Update the per-index indisreplident flags correctly.
 	 */
 	pg_index = table_open(IndexRelationId, RowExclusiveLock);
 	foreach(index, RelationGetIndexList(rel))
@@ -15843,19 +15823,23 @@ relation_mark_replica_identity(Relation rel, char ri_type, Oid indexOid,
 			elog(ERROR, "cache lookup failed for index %u", thisIndexOid);
 		pg_index_form = (Form_pg_index) GETSTRUCT(pg_index_tuple);
 
-		/*
-		 * Unset the bit if set.  We know it's wrong because we checked this
-		 * earlier.
-		 */
-		if (pg_index_form->indisreplident)
+		if (thisIndexOid == indexOid)
 		{
-			dirty = true;
-			pg_index_form->indisreplident = false;
+			/* Set the bit if not already set. */
+			if (!pg_index_form->indisreplident)
+			{
+				dirty = true;
+				pg_index_form->indisreplident = true;
+			}
 		}
-		else if (thisIndexOid == indexOid)
+		else
 		{
-			dirty = true;
-			pg_index_form->indisreplident = true;
+			/* Unset the bit if set. */
+			if (pg_index_form->indisreplident)
+			{
+				dirty = true;
+				pg_index_form->indisreplident = false;
+			}
 		}
 
 		if (dirty)
@@ -15867,7 +15851,9 @@ relation_mark_replica_identity(Relation rel, char ri_type, Oid indexOid,
 			/*
 			 * Invalidate the relcache for the table, so that after we commit
 			 * all sessions will refresh the table's replica identity index
-			 * before attempting any UPDATE or DELETE on the table.
+			 * before attempting any UPDATE or DELETE on the table.  (If we
+			 * changed the table's pg_class row above, then a relcache inval
+			 * is already queued due to that; but we might not have.)
 			 */
 			CacheInvalidateRelcache(rel);
 		}
@@ -15952,12 +15938,6 @@ ATExecReplicaIdentity(Relation rel, ReplicaIdentityStmt *stmt, LOCKMODE lockmode
 				(errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
 				 errmsg("cannot use partial index \"%s\" as replica identity",
 						RelationGetRelationName(indexRel))));
-	/* And neither are invalid indexes. */
-	if (!indexRel->rd_index->indisvalid)
-		ereport(ERROR,
-				(errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
-				 errmsg("cannot use invalid index \"%s\" as replica identity",
-						RelationGetRelationName(indexRel))));
 
 	/* Check index for nullable columns. */
 	for (key = 0; key < IndexRelationGetNumberOfKeyAttributes(indexRel); key++)