diff --git a/src/backend/parser/gram.y b/src/backend/parser/gram.y
index ace4fb5c77..dfb0d85d66 100644
--- a/src/backend/parser/gram.y
+++ b/src/backend/parser/gram.y
@@ -564,7 +564,7 @@ static Node *makeRecursiveViewSelect(char *relname, List *aliases, Node *query);
 %type <defelt>	generic_option_elem alter_generic_option_elem
 %type <list>	generic_option_list alter_generic_option_list
 
-%type <ival>	reindex_target_type
+%type <ival>	reindex_target_relation reindex_target_all
 %type <list>	opt_reindex_option_list
 
 %type <node>	copy_generic_opt_arg copy_generic_opt_arg_list_item
@@ -9092,13 +9092,12 @@ DropTransformStmt: DROP TRANSFORM opt_if_exists FOR Typename LANGUAGE name opt_d
  *
  *		QUERY:
  *
- *		REINDEX [ (options) ] {TABLE | INDEX | SCHEMA} [CONCURRENTLY] <name>
- *		REINDEX [ (options) ] DATABASE [CONCURRENTLY] [<name>]
- *		REINDEX [ (options) ] SYSTEM [<name>]
+ *		REINDEX [ (options) ] {INDEX | TABLE | SCHEMA} [CONCURRENTLY] <name>
+ *		REINDEX [ (options) ] {DATABASE | SYSTEM} [CONCURRENTLY] [<name>]
  *****************************************************************************/
 
 ReindexStmt:
-			REINDEX opt_reindex_option_list reindex_target_type opt_concurrently qualified_name
+			REINDEX opt_reindex_option_list reindex_target_relation opt_concurrently qualified_name
 				{
 					ReindexStmt *n = makeNode(ReindexStmt);
 
@@ -9124,29 +9123,27 @@ ReindexStmt:
 											makeDefElem("concurrently", NULL, @4));
 					$$ = (Node *) n;
 				}
-			| REINDEX opt_reindex_option_list DATABASE opt_concurrently opt_single_name
+			| REINDEX opt_reindex_option_list reindex_target_all opt_concurrently opt_single_name
 				{
 					ReindexStmt *n = makeNode(ReindexStmt);
-					n->kind = REINDEX_OBJECT_DATABASE;
-					n->name = NULL;
-					n->relation = NULL;
-					n->params = $2;
-					$$ = (Node *) n;
-				}
-			| REINDEX opt_reindex_option_list SYSTEM_P opt_single_name
-				{
-					ReindexStmt *n = makeNode(ReindexStmt);
-					n->kind = REINDEX_OBJECT_SYSTEM;
-					n->name = NULL;
+					n->kind = $3;
+					n->name = $5;
 					n->relation = NULL;
 					n->params = $2;
+					if ($4)
+						n->params = lappend(n->params,
+											makeDefElem("concurrently", NULL, @4));
 					$$ = (Node *) n;
 				}
 		;
-reindex_target_type:
+reindex_target_relation:
 			INDEX					{ $$ = REINDEX_OBJECT_INDEX; }
 			| TABLE					{ $$ = REINDEX_OBJECT_TABLE; }
 		;
+reindex_target_all:
+			SYSTEM_P				{ $$ = REINDEX_OBJECT_SYSTEM; }
+			| DATABASE				{ $$ = REINDEX_OBJECT_DATABASE; }
+		;
 opt_reindex_option_list:
 			'(' utility_option_list ')'				{ $$ = $2; }
 			| /* EMPTY */							{ $$ = NULL; }
diff --git a/src/test/regress/expected/create_index.out b/src/test/regress/expected/create_index.out
index a913a1846f..801b396398 100644
--- a/src/test/regress/expected/create_index.out
+++ b/src/test/regress/expected/create_index.out
@@ -2521,9 +2521,7 @@ ERROR:  cannot reindex system catalogs concurrently
 REINDEX INDEX CONCURRENTLY pg_toast.pg_toast_1260_index; -- no catalog toast index
 ERROR:  cannot reindex system catalogs concurrently
 REINDEX SYSTEM CONCURRENTLY postgres; -- not allowed for SYSTEM
-ERROR:  syntax error at or near "CONCURRENTLY"
-LINE 1: REINDEX SYSTEM CONCURRENTLY postgres;
-                       ^
+ERROR:  cannot reindex system catalogs concurrently
 REINDEX (CONCURRENTLY) SYSTEM postgres; -- ditto
 ERROR:  cannot reindex system catalogs concurrently
 REINDEX (CONCURRENTLY) SYSTEM;  -- ditto
diff --git a/doc/src/sgml/ref/reindex.sgml b/doc/src/sgml/ref/reindex.sgml
index 6750eb6e47..fcbda88149 100644
--- a/doc/src/sgml/ref/reindex.sgml
+++ b/doc/src/sgml/ref/reindex.sgml
@@ -22,8 +22,7 @@ PostgreSQL documentation
  <refsynopsisdiv>
 <synopsis>
 REINDEX [ ( <replaceable class="parameter">option</replaceable> [, ...] ) ] { INDEX | TABLE | SCHEMA } [ CONCURRENTLY ] <replaceable class="parameter">name</replaceable>
-REINDEX [ ( <replaceable class="parameter">option</replaceable> [, ...] ) ] DATABASE [ CONCURRENTLY ] [ <replaceable class="parameter">name</replaceable> ]
-REINDEX [ ( <replaceable class="parameter">option</replaceable> [, ...] ) ] SYSTEM [ <replaceable class="parameter">name</replaceable> ]
+REINDEX [ ( <replaceable class="parameter">option</replaceable> [, ...] ) ] { DATABASE | SYSTEM } [ CONCURRENTLY ] [ <replaceable class="parameter">name</replaceable> ]
 
 <phrase>where <replaceable class="parameter">option</replaceable> can be one of:</phrase>