diff --git a/src/backend/commands/repack.c b/src/backend/commands/repack.c
index 94f2eaa2346..ec100e3eef5 100644
--- a/src/backend/commands/repack.c
+++ b/src/backend/commands/repack.c
@@ -901,7 +901,7 @@ check_concurrent_repack_requirements(Relation rel, Oid *ident_idx_p)
 	if (wal_level < WAL_LEVEL_REPLICA)
 		ereport(ERROR,
 				errcode(ERRCODE_INVALID_PARAMETER_VALUE),
-				errmsg("cannot execute \"%s\" in this configuration",
+				errmsg("cannot execute %s in this configuration",
 					   "REPACK (CONCURRENTLY)"),
 				errdetail("%s requires \"wal_level\" to be set to \"replica\" or higher.",
 						  "REPACK (CONCURRENTLY)"));
@@ -910,8 +910,8 @@ check_concurrent_repack_requirements(Relation rel, Oid *ident_idx_p)
 	if (IsCatalogRelation(rel))
 		ereport(ERROR,
 				errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
-				errmsg("cannot repack relation \"%s\"",
-					   RelationGetRelationName(rel)),
+				errmsg("cannot execute %s on relation \"%s\"",
+					   "REPACK (CONCURRENTLY)", RelationGetRelationName(rel)),
 				errhint("%s is not supported for catalog relations.",
 						"REPACK (CONCURRENTLY)"));
 
@@ -922,8 +922,8 @@ check_concurrent_repack_requirements(Relation rel, Oid *ident_idx_p)
 	if (IsToastRelation(rel))
 		ereport(ERROR,
 				errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
-				errmsg("cannot repack relation \"%s\"",
-					   RelationGetRelationName(rel)),
+				errmsg("cannot execute %s on relation \"%s\"",
+					   "REPACK (CONCURRENTLY)", RelationGetRelationName(rel)),
 				errhint("%s is not supported for TOAST relations.",
 						"REPACK (CONCURRENTLY)"));
 
@@ -931,20 +931,26 @@ check_concurrent_repack_requirements(Relation rel, Oid *ident_idx_p)
 	if (relpersistence != RELPERSISTENCE_PERMANENT)
 		ereport(ERROR,
 				errcode(ERRCODE_OBJECT_NOT_IN_PREREQUISITE_STATE),
-				errmsg("cannot repack relation \"%s\"",
-					   RelationGetRelationName(rel)),
+				errmsg("cannot execute %s on relation \"%s\"",
+					   "REPACK (CONCURRENTLY)", RelationGetRelationName(rel)),
 				errhint("%s is only allowed for permanent relations.",
 						"REPACK (CONCURRENTLY)"));
 
-	/* With NOTHING, WAL does not contain the old tuple. */
+	/*
+	 * With NOTHING, WAL does not contain the old tuple; FULL is not yet
+	 * supported.
+	 */
 	replident = rel->rd_rel->relreplident;
-	if (replident == REPLICA_IDENTITY_NOTHING)
+	if (replident == REPLICA_IDENTITY_NOTHING ||
+		replident == REPLICA_IDENTITY_FULL)
 		ereport(ERROR,
 				errcode(ERRCODE_OBJECT_NOT_IN_PREREQUISITE_STATE),
-				errmsg("cannot repack relation \"%s\"",
-					   RelationGetRelationName(rel)),
-				errhint("Relation \"%s\" has insufficient replication identity.",
-						RelationGetRelationName(rel)));
+				errmsg("cannot execute %s on relation \"%s\"",
+					   "REPACK (CONCURRENTLY)", RelationGetRelationName(rel)),
+				errdetail("%s does not support tables with %s.",
+						  "REPACK (CONCURRENTLY)",
+						  replident == REPLICA_IDENTITY_NOTHING ?
+						  "REPLICA IDENTITY NOTHING" : "REPLICA IDENTITY FULL"));
 
 	/*
 	 * Obtain the replica identity index -- either one that has been set
@@ -955,12 +961,25 @@ check_concurrent_repack_requirements(Relation rel, Oid *ident_idx_p)
 	 */
 	ident_idx = GetRelationIdentityOrPK(rel);
 	if (!OidIsValid(ident_idx))
+	{
+		/* This special case warrants its own error message */
+		if (OidIsValid(rel->rd_pkindex) && rel->rd_ispkdeferrable)
+			ereport(ERROR,
+					errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
+					errmsg("cannot execute %s on relation \"%s\"",
+						   "REPACK (CONCURRENTLY)",
+						   RelationGetRelationName(rel)),
+					errdetail("%s does not support deferrable primary keys.",
+							  "REPACK (CONCURRENTLY)"),
+					errhint("Use ALTER TABLE ... REPLICA IDENTITY USING INDEX to designate another index as replica identity."));
+
 		ereport(ERROR,
 				errcode(ERRCODE_OBJECT_NOT_IN_PREREQUISITE_STATE),
-				errmsg("cannot process relation \"%s\"",
-					   RelationGetRelationName(rel)),
+				errmsg("cannot execute %s on relation \"%s\"",
+					   "REPACK (CONCURRENTLY)", RelationGetRelationName(rel)),
 				errhint("Relation \"%s\" has no identity index.",
 						RelationGetRelationName(rel)));
+	}
 
 	*ident_idx_p = ident_idx;
 }
diff --git a/src/test/regress/expected/cluster.out b/src/test/regress/expected/cluster.out
index 504ac1a3131..23f312c62a3 100644
--- a/src/test/regress/expected/cluster.out
+++ b/src/test/regress/expected/cluster.out
@@ -801,7 +801,7 @@ ORDER BY o.relname;
 --
 -- Disallowed in catalogs
 REPACK (CONCURRENTLY) pg_class;
-ERROR:  cannot repack relation "pg_class"
+ERROR:  cannot execute REPACK (CONCURRENTLY) on relation "pg_class"
 HINT:  REPACK (CONCURRENTLY) is not supported for catalog relations.
 -- Doesn't like partitioned tables
 REPACK (CONCURRENTLY) clstrpart;
@@ -809,17 +809,17 @@ ERROR:  REPACK (CONCURRENTLY) is not supported for partitioned tables
 HINT:  Consider running the command on individual partitions.
 -- Doesn't support catalog tables
 REPACK (CONCURRENTLY) pg_class;
-ERROR:  cannot repack relation "pg_class"
+ERROR:  cannot execute REPACK (CONCURRENTLY) on relation "pg_class"
 HINT:  REPACK (CONCURRENTLY) is not supported for catalog relations.
 -- Only support permanent tables, temp and unlogged tables are not supported
 CREATE TEMP TABLE repack_conc_temp (i int PRIMARY KEY);
 REPACK (CONCURRENTLY) repack_conc_temp;
-ERROR:  cannot repack relation "repack_conc_temp"
+ERROR:  cannot execute REPACK (CONCURRENTLY) on relation "repack_conc_temp"
 HINT:  REPACK (CONCURRENTLY) is only allowed for permanent relations.
 DROP TABLE repack_conc_temp;
 CREATE UNLOGGED TABLE repack_conc_unlogged (i int PRIMARY KEY);
 REPACK (CONCURRENTLY) repack_conc_unlogged;
-ERROR:  cannot repack relation "repack_conc_unlogged"
+ERROR:  cannot execute REPACK (CONCURRENTLY) on relation "repack_conc_unlogged"
 HINT:  REPACK (CONCURRENTLY) is only allowed for permanent relations.
 DROP TABLE repack_conc_unlogged;
 -- Doesn't support TOAST tables directly
@@ -835,19 +835,20 @@ DROP TABLE repack_conc_toast;
 CREATE TABLE repack_conc_replident (i int PRIMARY KEY);
 ALTER TABLE repack_conc_replident REPLICA IDENTITY NOTHING;
 REPACK (CONCURRENTLY) repack_conc_replident;
-ERROR:  cannot repack relation "repack_conc_replident"
-HINT:  Relation "repack_conc_replident" has insufficient replication identity.
+ERROR:  cannot execute REPACK (CONCURRENTLY) on relation "repack_conc_replident"
+DETAIL:  REPACK (CONCURRENTLY) does not support tables with REPLICA IDENTITY NOTHING.
 -- Doesn't support tables without a primary key or replica identity index
 ALTER TABLE repack_conc_replident DROP CONSTRAINT repack_conc_replident_pkey;
 ALTER TABLE repack_conc_replident REPLICA IDENTITY DEFAULT;
 REPACK (CONCURRENTLY) repack_conc_replident;
-ERROR:  cannot process relation "repack_conc_replident"
+ERROR:  cannot execute REPACK (CONCURRENTLY) on relation "repack_conc_replident"
 HINT:  Relation "repack_conc_replident" has no identity index.
 -- Doesn't support tables with deferrable primary keys
 ALTER TABLE repack_conc_replident ADD PRIMARY KEY (i) DEFERRABLE;
 REPACK (CONCURRENTLY) repack_conc_replident;
-ERROR:  cannot process relation "repack_conc_replident"
-HINT:  Relation "repack_conc_replident" has no identity index.
+ERROR:  cannot execute REPACK (CONCURRENTLY) on relation "repack_conc_replident"
+DETAIL:  REPACK (CONCURRENTLY) does not support deferrable primary keys.
+HINT:  Use ALTER TABLE ... REPLICA IDENTITY USING INDEX to designate another index as replica identity.
 -- clean up
 DROP TABLE repack_conc_replident;
 DROP TABLE clustertest;