diff --git a/pkg/sql/alter_table.go b/pkg/sql/alter_table.go
index 36a9a6bb39ec..358ad123df84 100644
--- a/pkg/sql/alter_table.go
+++ b/pkg/sql/alter_table.go
@@ -98,11 +98,11 @@ func (n *alterTableNode) startExec(params runParams) error {
 			d := t.ColumnDef
 			if len(d.CheckExprs) > 0 {
 				return pgerror.UnimplementedWithIssueError(29639,
-					"adding a CHECK constraint via ALTER not supported")
+					"adding a CHECK constraint while also adding a column via ALTER not supported")
 			}
 			if d.HasFKConstraint() {
-				return pgerror.UnimplementedWithIssueError(8855,
-					"adding a REFERENCES constraint via ALTER not supported")
+				return pgerror.UnimplementedWithIssueError(32917,
+					"adding a REFERENCES constraint while also adding a column via ALTER not supported")
 			}
 
 			newDef, seqDbDesc, seqName, seqOpts, err := params.p.processSerialInColumnDef(params.ctx, d, tn)
diff --git a/pkg/sql/logictest/testdata/logic_test/alter_table b/pkg/sql/logictest/testdata/logic_test/alter_table
index 7ff787ae7777..922f5432d63c 100644
--- a/pkg/sql/logictest/testdata/logic_test/alter_table
+++ b/pkg/sql/logictest/testdata/logic_test/alter_table
@@ -349,10 +349,10 @@ ALTER TABLE o DROP COLUMN h
 statement ok
 ALTER TABLE o DROP COLUMN h CASCADE
 
-statement error adding a CHECK constraint via ALTER not supported
+statement error adding a CHECK constraint while also adding a column via ALTER not supported
 ALTER TABLE t ADD f INT CHECK (f>1)
 
-statement error adding a REFERENCES constraint via ALTER not supported
+statement error adding a REFERENCES constraint while also adding a column via ALTER not supported
 ALTER TABLE t ADD f INT UNIQUE REFERENCES other
 
 # Test that more than one column with constraints can be added in the same