diff --git a/src/bin/psql/tab-complete.c b/src/bin/psql/tab-complete.c
index 9dbd555166..31f4b7d862 100644
--- a/src/bin/psql/tab-complete.c
+++ b/src/bin/psql/tab-complete.c
@@ -1554,9 +1554,18 @@ psql_completion(const char *text, int start, int end)
 		COMPLETE_WITH("PARTITION");
 	else if (Matches("ALTER", "INDEX", MatchAny, "ATTACH", "PARTITION"))
 		COMPLETE_WITH_SCHEMA_QUERY(Query_for_list_of_indexes, NULL);
-	/* ALTER INDEX <name> ALTER COLUMN <colnum> */
-	else if (Matches("ALTER", "INDEX", MatchAny, "ALTER", "COLUMN", MatchAny))
+	/* ALTER INDEX <name> ALTER [COLUMN] */
+	else if (Matches("ALTER", "INDEX", MatchAny, "ALTER", "COLUMN") ||
+			 Matches("ALTER", "INDEX", MatchAny, "ALTER"))
+		COMPLETE_WITH_ATTR(prev3_wd, "");
+	/* ALTER INDEX <name> ALTER [COLUMN] <colname> */
+	else if (Matches("ALTER", "INDEX", MatchAny, "ALTER", "COLUMN", MatchAny) ||
+			 Matches("ALTER", "INDEX", MatchAny, "ALTER", MatchAny))
 		COMPLETE_WITH("SET STATISTICS");
+	/* ALTER INDEX <name> ALTER COLUMN <colname> SET STATISTICS */
+	else if (HeadMatches("ALTER", "INDEX") && TailMatches("SET", "STATISTICS")){
+		/* We don't complete after "SET STATISTICS" */
+	}
 	/* ALTER INDEX <name> SET */
 	else if (Matches("ALTER", "INDEX", MatchAny, "SET"))
 		COMPLETE_WITH("(", "TABLESPACE");