diff --git a/.unreleased/pr_6754 b/.unreleased/pr_6754
new file mode 100644
index 000000000..b1d7d1569
--- /dev/null
+++ b/.unreleased/pr_6754
@@ -0,0 +1 @@
+Implements: #6754 Allow DROP CONSTRAINT on compressed hypertables
diff --git a/src/process_utility.c b/src/process_utility.c
index a50bc8d0d..bd7140df4 100644
--- a/src/process_utility.c
+++ b/src/process_utility.c
@@ -250,10 +250,11 @@ check_alter_table_allowed_on_ht_with_compression(Hypertable *ht, AlterTableStmt
 				/* this is passed down in `process_altertable_change_owner` */
 			case AT_SetTableSpace:
 				/* this is passed down in `process_altertable_set_tablespace_end` */
-			case AT_SetStatistics: /* should this be pushed down in some way? */
-			case AT_AddColumn:	   /* this is passed down */
-			case AT_ColumnDefault: /* this is passed down */
-			case AT_DropColumn:	   /* this is passed down */
+			case AT_SetStatistics:	/* should this be pushed down in some way? */
+			case AT_AddColumn:		/* this is passed down */
+			case AT_ColumnDefault:	/* this is passed down */
+			case AT_DropColumn:		/* this is passed down */
+			case AT_DropConstraint: /* this is passed down */
 #if PG14_GE
 			case AT_ReAddStatistics:
 			case AT_SetCompression:
diff --git a/tsl/test/expected/compression_errors-13.out b/tsl/test/expected/compression_errors-13.out
index 06b046f9c..fd931ce00 100644
--- a/tsl/test/expected/compression_errors-13.out
+++ b/tsl/test/expected/compression_errors-13.out
@@ -208,8 +208,10 @@ ALTER TABLE foo ADD CONSTRAINT chk CHECK(b > 0);
 ERROR:  operation not supported on hypertables that have compression enabled
 ALTER TABLE foo ADD CONSTRAINT chk UNIQUE(b);
 ERROR:  operation not supported on hypertables that have compression enabled
+--should succeed
+BEGIN;
 ALTER TABLE foo DROP CONSTRAINT chk_existing;
-ERROR:  operation not supported on hypertables that have compression enabled
+ROLLBACK;
 --note that the time column "a" should not be added to the end of the order by list again (should appear first)
 SELECT * FROM _timescaledb_catalog.compression_settings WHERE relid = 'foo'::regclass;
  relid | segmentby | orderby | orderby_desc | orderby_nullsfirst 
diff --git a/tsl/test/expected/compression_errors-14.out b/tsl/test/expected/compression_errors-14.out
index 06b046f9c..fd931ce00 100644
--- a/tsl/test/expected/compression_errors-14.out
+++ b/tsl/test/expected/compression_errors-14.out
@@ -208,8 +208,10 @@ ALTER TABLE foo ADD CONSTRAINT chk CHECK(b > 0);
 ERROR:  operation not supported on hypertables that have compression enabled
 ALTER TABLE foo ADD CONSTRAINT chk UNIQUE(b);
 ERROR:  operation not supported on hypertables that have compression enabled
+--should succeed
+BEGIN;
 ALTER TABLE foo DROP CONSTRAINT chk_existing;
-ERROR:  operation not supported on hypertables that have compression enabled
+ROLLBACK;
 --note that the time column "a" should not be added to the end of the order by list again (should appear first)
 SELECT * FROM _timescaledb_catalog.compression_settings WHERE relid = 'foo'::regclass;
  relid | segmentby | orderby | orderby_desc | orderby_nullsfirst 
diff --git a/tsl/test/expected/compression_errors-15.out b/tsl/test/expected/compression_errors-15.out
index 06b046f9c..fd931ce00 100644
--- a/tsl/test/expected/compression_errors-15.out
+++ b/tsl/test/expected/compression_errors-15.out
@@ -208,8 +208,10 @@ ALTER TABLE foo ADD CONSTRAINT chk CHECK(b > 0);
 ERROR:  operation not supported on hypertables that have compression enabled
 ALTER TABLE foo ADD CONSTRAINT chk UNIQUE(b);
 ERROR:  operation not supported on hypertables that have compression enabled
+--should succeed
+BEGIN;
 ALTER TABLE foo DROP CONSTRAINT chk_existing;
-ERROR:  operation not supported on hypertables that have compression enabled
+ROLLBACK;
 --note that the time column "a" should not be added to the end of the order by list again (should appear first)
 SELECT * FROM _timescaledb_catalog.compression_settings WHERE relid = 'foo'::regclass;
  relid | segmentby | orderby | orderby_desc | orderby_nullsfirst 
diff --git a/tsl/test/expected/compression_errors-16.out b/tsl/test/expected/compression_errors-16.out
index afd3dd9a4..15050c2b9 100644
--- a/tsl/test/expected/compression_errors-16.out
+++ b/tsl/test/expected/compression_errors-16.out
@@ -208,8 +208,10 @@ ALTER TABLE foo ADD CONSTRAINT chk CHECK(b > 0);
 ERROR:  operation not supported on hypertables that have compression enabled
 ALTER TABLE foo ADD CONSTRAINT chk UNIQUE(b);
 ERROR:  operation not supported on hypertables that have compression enabled
+--should succeed
+BEGIN;
 ALTER TABLE foo DROP CONSTRAINT chk_existing;
-ERROR:  operation not supported on hypertables that have compression enabled
+ROLLBACK;
 --note that the time column "a" should not be added to the end of the order by list again (should appear first)
 SELECT * FROM _timescaledb_catalog.compression_settings WHERE relid = 'foo'::regclass;
  relid | segmentby | orderby | orderby_desc | orderby_nullsfirst 
diff --git a/tsl/test/sql/compression_errors.sql.in b/tsl/test/sql/compression_errors.sql.in
index a81f2b8fd..6a70f3c3d 100644
--- a/tsl/test/sql/compression_errors.sql.in
+++ b/tsl/test/sql/compression_errors.sql.in
@@ -112,7 +112,11 @@ ALTER TABLE foo ALTER COLUMN t SET NOT NULL;
 ALTER TABLE foo RESET (timescaledb.compress);
 ALTER TABLE foo ADD CONSTRAINT chk CHECK(b > 0);
 ALTER TABLE foo ADD CONSTRAINT chk UNIQUE(b);
+
+--should succeed
+BEGIN;
 ALTER TABLE foo DROP CONSTRAINT chk_existing;
+ROLLBACK;
 
 --note that the time column "a" should not be added to the end of the order by list again (should appear first)
 SELECT * FROM _timescaledb_catalog.compression_settings WHERE relid = 'foo'::regclass;