diff --git a/src/test/regress/expected/timestamp.out b/src/test/regress/expected/timestamp.out
index c9e768461a..9405e8ba1c 100644
--- a/src/test/regress/expected/timestamp.out
+++ b/src/test/regress/expected/timestamp.out
@@ -7,6 +7,8 @@ CREATE TABLE TIMESTAMP_TBL ( d1 timestamp(2) without time zone);
 -- Shorthand values
 -- Not directly usable for regression testing since these are not constants.
 -- So, just try to test parser and hope for the best - thomas 97/04/26
+-- NB: could get a failure if local midnight passes during the next few
+-- statements.
 INSERT INTO TIMESTAMP_TBL VALUES ('now');
 INSERT INTO TIMESTAMP_TBL VALUES ('current');
 INSERT INTO TIMESTAMP_TBL VALUES ('today');
@@ -43,7 +45,7 @@ DELETE FROM TIMESTAMP_TBL;
 BEGIN;
 INSERT INTO TIMESTAMP_TBL VALUES ('now');
 INSERT INTO TIMESTAMP_TBL VALUES ('now');
-SELECT count(*) AS two FROM TIMESTAMP_TBL WHERE d1 = timestamp without time zone 'now';
+SELECT count(*) AS two FROM TIMESTAMP_TBL WHERE d1 = timestamp(2) without time zone 'now';
  two 
 -----
    2
diff --git a/src/test/regress/expected/timestamptz.out b/src/test/regress/expected/timestamptz.out
index 142eb2508c..ed11d1629d 100644
--- a/src/test/regress/expected/timestamptz.out
+++ b/src/test/regress/expected/timestamptz.out
@@ -40,7 +40,7 @@ DELETE FROM TIMESTAMPTZ_TBL;
 BEGIN;
 INSERT INTO TIMESTAMPTZ_TBL VALUES ('now');
 INSERT INTO TIMESTAMPTZ_TBL VALUES ('now');
-SELECT count(*) AS two FROM TIMESTAMPTZ_TBL WHERE d1 = timestamp with time zone 'now';
+SELECT count(*) AS two FROM TIMESTAMPTZ_TBL WHERE d1 = timestamp(2) with time zone 'now';
  two 
 -----
    2
diff --git a/src/test/regress/sql/timestamp.sql b/src/test/regress/sql/timestamp.sql
index df1adf9522..b08e81e80e 100644
--- a/src/test/regress/sql/timestamp.sql
+++ b/src/test/regress/sql/timestamp.sql
@@ -9,6 +9,8 @@ CREATE TABLE TIMESTAMP_TBL ( d1 timestamp(2) without time zone);
 -- Shorthand values
 -- Not directly usable for regression testing since these are not constants.
 -- So, just try to test parser and hope for the best - thomas 97/04/26
+-- NB: could get a failure if local midnight passes during the next few
+-- statements.
 
 INSERT INTO TIMESTAMP_TBL VALUES ('now');
 INSERT INTO TIMESTAMP_TBL VALUES ('current');
@@ -29,7 +31,7 @@ DELETE FROM TIMESTAMP_TBL;
 BEGIN;
 INSERT INTO TIMESTAMP_TBL VALUES ('now');
 INSERT INTO TIMESTAMP_TBL VALUES ('now');
-SELECT count(*) AS two FROM TIMESTAMP_TBL WHERE d1 = timestamp without time zone 'now';
+SELECT count(*) AS two FROM TIMESTAMP_TBL WHERE d1 = timestamp(2) without time zone 'now';
 END;
 DELETE FROM TIMESTAMP_TBL;
 
diff --git a/src/test/regress/sql/timestamptz.sql b/src/test/regress/sql/timestamptz.sql
index 13ffb379a2..e60bacb962 100644
--- a/src/test/regress/sql/timestamptz.sql
+++ b/src/test/regress/sql/timestamptz.sql
@@ -25,7 +25,7 @@ DELETE FROM TIMESTAMPTZ_TBL;
 BEGIN;
 INSERT INTO TIMESTAMPTZ_TBL VALUES ('now');
 INSERT INTO TIMESTAMPTZ_TBL VALUES ('now');
-SELECT count(*) AS two FROM TIMESTAMPTZ_TBL WHERE d1 = timestamp with time zone 'now';
+SELECT count(*) AS two FROM TIMESTAMPTZ_TBL WHERE d1 = timestamp(2) with time zone 'now';
 END;
 DELETE FROM TIMESTAMPTZ_TBL;