diff --git a/src/backend/catalog/heap.c b/src/backend/catalog/heap.c
index ab3d83f29b..0f1547b567 100644
--- a/src/backend/catalog/heap.c
+++ b/src/backend/catalog/heap.c
@@ -52,7 +52,6 @@
 #include "catalog/pg_opclass.h"
 #include "catalog/pg_partitioned_table.h"
 #include "catalog/pg_statistic.h"
-#include "catalog/pg_statistic_ext.h"
 #include "catalog/pg_subscription_rel.h"
 #include "catalog/pg_tablespace.h"
 #include "catalog/pg_type.h"
@@ -1615,10 +1614,7 @@ RemoveAttributeById(Oid relid, AttrNumber attnum)
 	heap_close(attr_rel, RowExclusiveLock);
 
 	if (attnum > 0)
-	{
 		RemoveStatistics(relid, attnum);
-		RemoveStatisticsExt(relid, attnum);
-	}
 
 	relation_close(rel, NoLock);
 }
@@ -1873,7 +1869,6 @@ heap_drop_with_catalog(Oid relid)
 	 * delete statistics
 	 */
 	RemoveStatistics(relid, 0);
-	RemoveStatisticsExt(relid, 0);
 
 	/*
 	 * delete attribute tuples
@@ -2785,75 +2780,6 @@ RemoveStatistics(Oid relid, AttrNumber attnum)
 }
 
 
-/*
- * RemoveStatisticsExt --- remove entries in pg_statistic_ext for a relation
- *
- * If attnum is zero, remove all entries for rel; else remove only the
- * one(s) involving that column.
- */
-void
-RemoveStatisticsExt(Oid relid, AttrNumber attnum)
-{
-	Relation	pgstatisticext;
-	SysScanDesc scan;
-	ScanKeyData key;
-	HeapTuple	tuple;
-
-	/*
-	 * Scan pg_statistic_ext to delete relevant tuples
-	 */
-	pgstatisticext = heap_open(StatisticExtRelationId, RowExclusiveLock);
-
-	ScanKeyInit(&key,
-				Anum_pg_statistic_ext_stxrelid,
-				BTEqualStrategyNumber, F_OIDEQ,
-				ObjectIdGetDatum(relid));
-
-	scan = systable_beginscan(pgstatisticext,
-							  StatisticExtRelidIndexId,
-							  true, NULL, 1, &key);
-
-	while (HeapTupleIsValid(tuple = systable_getnext(scan)))
-	{
-		bool		delete = false;
-
-		if (attnum == 0)
-			delete = true;
-		else if (attnum != 0)
-		{
-			Form_pg_statistic_ext	staForm;
-			int			i;
-
-			/*
-			 * Decode the stxkeys array and delete any stats that involve the
-			 * specified column.
-			 */
-			staForm = (Form_pg_statistic_ext) GETSTRUCT(tuple);
-			for (i = 0; i < staForm->stxkeys.dim1; i++)
-			{
-				if (staForm->stxkeys.values[i] == attnum)
-				{
-					delete = true;
-					break;
-				}
-			}
-		}
-
-		if (delete)
-		{
-			CatalogTupleDelete(pgstatisticext, &tuple->t_self);
-			deleteDependencyRecordsFor(StatisticExtRelationId,
-									   HeapTupleGetOid(tuple),
-									   false);
-		}
-	}
-
-	systable_endscan(scan);
-
-	heap_close(pgstatisticext, RowExclusiveLock);
-}
-
-
 /*
  * RelationTruncateIndexes - truncate all indexes associated
  * with the heap relation to zero tuples.
diff --git a/src/backend/commands/statscmds.c b/src/backend/commands/statscmds.c
index 662b4fa15d..db5f4278d5 100644
--- a/src/backend/commands/statscmds.c
+++ b/src/backend/commands/statscmds.c
@@ -50,11 +50,11 @@ CreateStatistics(CreateStatsStmt *stmt)
 {
 	int16		attnums[STATS_MAX_DIMENSIONS];
 	int			numcols = 0;
-	ObjectAddress address = InvalidObjectAddress;
 	char	   *namestr;
 	NameData	stxname;
 	Oid			statoid;
 	Oid			namespaceId;
+	Oid			stxowner = GetUserId();
 	HeapTuple	htup;
 	Datum		values[Natts_pg_statistic_ext];
 	bool		nulls[Natts_pg_statistic_ext];
@@ -63,7 +63,7 @@ CreateStatistics(CreateStatsStmt *stmt)
 	Relation	rel = NULL;
 	Oid			relid;
 	ObjectAddress parentobject,
-				childobject;
+				myself;
 	Datum		types[2];		/* one for each possible type of statistics */
 	int			ntypes;
 	ArrayType  *stxkind;
@@ -140,7 +140,7 @@ CreateStatistics(CreateStatsStmt *stmt)
 							RelationGetRelationName(rel))));
 
 		/* You must own the relation to create stats on it */
-		if (!pg_class_ownercheck(RelationGetRelid(rel), GetUserId()))
+		if (!pg_class_ownercheck(RelationGetRelid(rel), stxowner))
 			aclcheck_error(ACLCHECK_NOT_OWNER, ACL_KIND_CLASS,
 						   RelationGetRelationName(rel));
 	}
@@ -185,7 +185,7 @@ CreateStatistics(CreateStatsStmt *stmt)
 		attForm = (Form_pg_attribute) GETSTRUCT(atttuple);
 
 		/* Disallow use of system attributes in extended stats */
-		if (attForm->attnum < 0)
+		if (attForm->attnum <= 0)
 			ereport(ERROR,
 					(errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
 					 errmsg("statistics creation on system columns is not supported")));
@@ -205,7 +205,7 @@ CreateStatistics(CreateStatsStmt *stmt)
 					 errmsg("cannot have more than %d columns in statistics",
 							STATS_MAX_DIMENSIONS)));
 
-		attnums[numcols] = ((Form_pg_attribute) GETSTRUCT(atttuple))->attnum;
+		attnums[numcols] = attForm->attnum;
 		numcols++;
 		ReleaseSysCache(atttuple);
 	}
@@ -231,10 +231,12 @@ CreateStatistics(CreateStatsStmt *stmt)
 	 * just check consecutive elements.
 	 */
 	for (i = 1; i < numcols; i++)
+	{
 		if (attnums[i] == attnums[i - 1])
 			ereport(ERROR,
 					(errcode(ERRCODE_DUPLICATE_COLUMN),
 				  errmsg("duplicate column name in statistics definition")));
+	}
 
 	/* Form an int2vector representation of the sorted column list */
 	stxkeys = buildint2vector(attnums, numcols);
@@ -288,7 +290,7 @@ CreateStatistics(CreateStatsStmt *stmt)
 	values[Anum_pg_statistic_ext_stxrelid - 1] = ObjectIdGetDatum(relid);
 	values[Anum_pg_statistic_ext_stxname - 1] = NameGetDatum(&stxname);
 	values[Anum_pg_statistic_ext_stxnamespace - 1] = ObjectIdGetDatum(namespaceId);
-	values[Anum_pg_statistic_ext_stxowner - 1] = ObjectIdGetDatum(GetUserId());
+	values[Anum_pg_statistic_ext_stxowner - 1] = ObjectIdGetDatum(stxowner);
 	values[Anum_pg_statistic_ext_stxkeys - 1] = PointerGetDatum(stxkeys);
 	values[Anum_pg_statistic_ext_stxkind - 1] = PointerGetDatum(stxkind);
 
@@ -312,29 +314,35 @@ CreateStatistics(CreateStatsStmt *stmt)
 	relation_close(rel, NoLock);
 
 	/*
-	 * Add a dependency on the table, so that stats get dropped on DROP TABLE.
-	 *
-	 * XXX don't we need dependencies on the specific columns, instead?
+	 * Add an AUTO dependency on each column used in the stats, so that the
+	 * stats object goes away if any or all of them get dropped.
 	 */
-	ObjectAddressSet(parentobject, RelationRelationId, relid);
-	ObjectAddressSet(childobject, StatisticExtRelationId, statoid);
-	recordDependencyOn(&childobject, &parentobject, DEPENDENCY_AUTO);
+	ObjectAddressSet(myself, StatisticExtRelationId, statoid);
+
+	for (i = 0; i < numcols; i++)
+	{
+		ObjectAddressSubSet(parentobject, RelationRelationId, relid, attnums[i]);
+		recordDependencyOn(&myself, &parentobject, DEPENDENCY_AUTO);
+	}
 
 	/*
-	 * Also add dependency on the schema.  This is required to ensure that we
-	 * drop the statistics on DROP SCHEMA.  This is not handled automatically
-	 * by DROP TABLE because the statistics might be in a different schema
-	 * from the table itself.  (This definition is a bit bizarre for the
-	 * single-table case, but it will make more sense if/when we support
-	 * extended stats across multiple tables.)
+	 * Also add dependencies on namespace and owner.  These are required
+	 * because the stats object might have a different namespace and/or owner
+	 * than the underlying table(s).
 	 */
 	ObjectAddressSet(parentobject, NamespaceRelationId, namespaceId);
-	recordDependencyOn(&childobject, &parentobject, DEPENDENCY_AUTO);
+	recordDependencyOn(&myself, &parentobject, DEPENDENCY_NORMAL);
+
+	recordDependencyOnOwner(StatisticExtRelationId, statoid, stxowner);
+
+	/*
+	 * XXX probably there should be a recordDependencyOnCurrentExtension call
+	 * here too, but we'd have to add support for ALTER EXTENSION ADD/DROP
+	 * STATISTICS, which is more work than it seems worth.
+	 */
 
 	/* Return stats object's address */
-	ObjectAddressSet(address, StatisticExtRelationId, statoid);
-
-	return address;
+	return myself;
 }
 
 /*
diff --git a/src/include/catalog/catversion.h b/src/include/catalog/catversion.h
index e91479e089..85ee2f6bde 100644
--- a/src/include/catalog/catversion.h
+++ b/src/include/catalog/catversion.h
@@ -53,6 +53,6 @@
  */
 
 /*							yyyymmddN */
-#define CATALOG_VERSION_NO	201705111
+#define CATALOG_VERSION_NO	201705121
 
 #endif
diff --git a/src/include/catalog/heap.h b/src/include/catalog/heap.h
index 473fe177ba..1187797fd9 100644
--- a/src/include/catalog/heap.h
+++ b/src/include/catalog/heap.h
@@ -119,7 +119,6 @@ extern void RemoveAttrDefault(Oid relid, AttrNumber attnum,
 				  DropBehavior behavior, bool complain, bool internal);
 extern void RemoveAttrDefaultById(Oid attrdefId);
 extern void RemoveStatistics(Oid relid, AttrNumber attnum);
-extern void RemoveStatisticsExt(Oid relid, AttrNumber attnum);
 
 extern Form_pg_attribute SystemAttributeDefinition(AttrNumber attno,
 						  bool relhasoids);
diff --git a/src/test/regress/expected/stats_ext.out b/src/test/regress/expected/stats_ext.out
index 4ccdf21a01..13780897c5 100644
--- a/src/test/regress/expected/stats_ext.out
+++ b/src/test/regress/expected/stats_ext.out
@@ -47,7 +47,7 @@ DROP STATISTICS regress_schema_2.ab1_a_b_stats;
 -- Ensure statistics are dropped when columns are
 CREATE STATISTICS ab1_b_c_stats ON b, c FROM ab1;
 CREATE STATISTICS ab1_a_b_c_stats ON a, b, c FROM ab1;
-CREATE STATISTICS ab1_a_b_stats ON a, b FROM ab1;
+CREATE STATISTICS ab1_b_a_stats ON b, a FROM ab1;
 ALTER TABLE ab1 DROP COLUMN a;
 \d ab1
                 Table "public.ab1"
@@ -58,7 +58,19 @@ ALTER TABLE ab1 DROP COLUMN a;
 Statistics:
     "public"."ab1_b_c_stats" (ndistinct, dependencies) ON b, c FROM ab1
 
+-- Ensure statistics are dropped when table is
+SELECT stxname FROM pg_statistic_ext WHERE stxname LIKE 'ab1%';
+    stxname    
+---------------
+ ab1_b_c_stats
+(1 row)
+
 DROP TABLE ab1;
+SELECT stxname FROM pg_statistic_ext WHERE stxname LIKE 'ab1%';
+ stxname 
+---------
+(0 rows)
+
 -- Ensure things work sanely with SET STATISTICS 0
 CREATE TABLE ab1 (a INTEGER, b INTEGER);
 ALTER TABLE ab1 ALTER a SET STATISTICS 0;
diff --git a/src/test/regress/sql/stats_ext.sql b/src/test/regress/sql/stats_ext.sql
index 4050f33c08..09b7d8e102 100644
--- a/src/test/regress/sql/stats_ext.sql
+++ b/src/test/regress/sql/stats_ext.sql
@@ -34,10 +34,13 @@ DROP STATISTICS regress_schema_2.ab1_a_b_stats;
 -- Ensure statistics are dropped when columns are
 CREATE STATISTICS ab1_b_c_stats ON b, c FROM ab1;
 CREATE STATISTICS ab1_a_b_c_stats ON a, b, c FROM ab1;
-CREATE STATISTICS ab1_a_b_stats ON a, b FROM ab1;
+CREATE STATISTICS ab1_b_a_stats ON b, a FROM ab1;
 ALTER TABLE ab1 DROP COLUMN a;
 \d ab1
+-- Ensure statistics are dropped when table is
+SELECT stxname FROM pg_statistic_ext WHERE stxname LIKE 'ab1%';
 DROP TABLE ab1;
+SELECT stxname FROM pg_statistic_ext WHERE stxname LIKE 'ab1%';
 
 -- Ensure things work sanely with SET STATISTICS 0
 CREATE TABLE ab1 (a INTEGER, b INTEGER);