diff --git a/src/backend/commands/indexcmds.c b/src/backend/commands/indexcmds.c
index 531a977fa0..3424954594 100644
--- a/src/backend/commands/indexcmds.c
+++ b/src/backend/commands/indexcmds.c
@@ -810,8 +810,7 @@ DefineIndex(Oid relationId,
 									key->partattrs[i] - 1);
 				ereport(ERROR,
 						(errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
-						 errmsg("insufficient columns in %s constraint definition",
-								constraint_type),
+						 errmsg("unique constraint on partitioned table must include all partitioning columns"),
 						 errdetail("%s constraint on table \"%s\" lacks column \"%s\" which is part of the partition key.",
 								   constraint_type, RelationGetRelationName(rel),
 								   NameStr(att->attname))));
diff --git a/src/test/regress/expected/indexing.out b/src/test/regress/expected/indexing.out
index 3cc78c1571..6d1c7105cd 100644
--- a/src/test/regress/expected/indexing.out
+++ b/src/test/regress/expected/indexing.out
@@ -855,16 +855,16 @@ Indexes:
 drop table idxpart;
 -- Failing to use the full partition key is not allowed
 create table idxpart (a int unique, b int) partition by range (a, b);
-ERROR:  insufficient columns in UNIQUE constraint definition
+ERROR:  unique constraint on partitioned table must include all partitioning columns
 DETAIL:  UNIQUE constraint on table "idxpart" lacks column "b" which is part of the partition key.
 create table idxpart (a int, b int unique) partition by range (a, b);
-ERROR:  insufficient columns in UNIQUE constraint definition
+ERROR:  unique constraint on partitioned table must include all partitioning columns
 DETAIL:  UNIQUE constraint on table "idxpart" lacks column "a" which is part of the partition key.
 create table idxpart (a int primary key, b int) partition by range (b, a);
-ERROR:  insufficient columns in PRIMARY KEY constraint definition
+ERROR:  unique constraint on partitioned table must include all partitioning columns
 DETAIL:  PRIMARY KEY constraint on table "idxpart" lacks column "b" which is part of the partition key.
 create table idxpart (a int, b int primary key) partition by range (b, a);
-ERROR:  insufficient columns in PRIMARY KEY constraint definition
+ERROR:  unique constraint on partitioned table must include all partitioning columns
 DETAIL:  PRIMARY KEY constraint on table "idxpart" lacks column "a" which is part of the partition key.
 -- OK if you use them in some other order
 create table idxpart (a int, b int, c text, primary key  (a, b, c)) partition by range (b, c, a);
@@ -884,7 +884,7 @@ DETAIL:  UNIQUE constraints cannot be used when partition keys include expressio
 -- use ALTER TABLE to add a primary key
 create table idxpart (a int, b int, c text) partition by range (a, b);
 alter table idxpart add primary key (a);	-- not an incomplete one though
-ERROR:  insufficient columns in PRIMARY KEY constraint definition
+ERROR:  unique constraint on partitioned table must include all partitioning columns
 DETAIL:  PRIMARY KEY constraint on table "idxpart" lacks column "b" which is part of the partition key.
 alter table idxpart add primary key (a, b);	-- this works
 \d idxpart
@@ -915,7 +915,7 @@ drop table idxpart;
 -- use ALTER TABLE to add a unique constraint
 create table idxpart (a int, b int) partition by range (a, b);
 alter table idxpart add unique (a);			-- not an incomplete one though
-ERROR:  insufficient columns in UNIQUE constraint definition
+ERROR:  unique constraint on partitioned table must include all partitioning columns
 DETAIL:  UNIQUE constraint on table "idxpart" lacks column "b" which is part of the partition key.
 alter table idxpart add unique (b, a);		-- this works
 \d idxpart
@@ -965,7 +965,7 @@ drop table idxpart;
 create table idxpart (a int, b int, primary key (a)) partition by range (a);
 create table idxpart2 partition of idxpart
 for values from (0) to (1000) partition by range (b); -- fail
-ERROR:  insufficient columns in PRIMARY KEY constraint definition
+ERROR:  unique constraint on partitioned table must include all partitioning columns
 DETAIL:  PRIMARY KEY constraint on table "idxpart2" lacks column "b" which is part of the partition key.
 drop table idxpart;
 -- Ditto for the ATTACH PARTITION case
@@ -973,7 +973,7 @@ create table idxpart (a int unique, b int) partition by range (a);
 create table idxpart1 (a int not null, b int, unique (a, b))
   partition by range (a, b);
 alter table idxpart attach partition idxpart1 for values from (1) to (1000);
-ERROR:  insufficient columns in UNIQUE constraint definition
+ERROR:  unique constraint on partitioned table must include all partitioning columns
 DETAIL:  UNIQUE constraint on table "idxpart1" lacks column "b" which is part of the partition key.
 DROP TABLE idxpart, idxpart1;
 -- Multi-layer partitioning works correctly in this case:
@@ -1426,7 +1426,7 @@ insert into covidxpart values (4, 1);
 ERROR:  duplicate key value violates unique constraint "covidxpart4_a_b_idx"
 DETAIL:  Key (a)=(4) already exists.
 create unique index on covidxpart (b) include (a); -- should fail
-ERROR:  insufficient columns in UNIQUE constraint definition
+ERROR:  unique constraint on partitioned table must include all partitioning columns
 DETAIL:  UNIQUE constraint on table "covidxpart" lacks column "a" which is part of the partition key.
 -- check that detaching a partition also detaches the primary key constraint
 create table parted_pk_detach_test (a int primary key) partition by list (a);