PostgreSQL 9.2 tstzrange null/infinity CONSTRAINT CHECK

I’d like to limit a PostgreSQL 9.2 tstzrange to valid dates at both ends. No NULLs nor ‘infinity’.

Various revisions of this SQL isn’t constraining ‘-/+infinity’ input:

CREATE TABLE bill
(
  id serial NOT NULL,
  created_at timestamp with time zone NOT NULL DEFAULT now(),
  period tstzrange NOT NULL,
  -- other columns
  CONSTRAINT bill_pk PRIMARY KEY (id),
  CONSTRAINT bill_period_lower_not_null_ck CHECK (lower(period) IS NOT NULL),
  CONSTRAINT bill_period_upper_not_null_ck CHECK (upper(period) IS NOT NULL),
  CONSTRAINT bill_period_lower_not_infinity_ck CHECK (lower_inf(period) IS FALSE),
  CONSTRAINT bill_period_upper_not_infinity_ck CHECK (upper_inf(period) IS FALSE)
);


INSERT INTO bill (period) VALUES (tstzrange (NULL, NULL));
INSERT INTO bill (period) VALUES (tstzrange ('2000-05-10', '2015-02-22');
INSERT INTO bill (period) VALUES (tstzrange ('2000-05-10', now());
INSERT INTO bill (period) VALUES (tstzrange ('infinity', now());
INSERT INTO bill (period) VALUES (tstzrange ('-infinity', now());
INSERT INTO bill (period) VALUES (tstzrange (now(), 'infinity');


psql (9.2.3)
Type "help" for help.

test_1=> SELECT id, period FROM bill;
 id |                           period
----+------------------------------------------------------------
  1 | ["2000-05-10 00:00:00+01","2015-02-22 00:00:00+00")
  2 | ["2000-05-10 00:00:00+01","2013-10-16 13:20:01.793803+01")
  4 | [-infinity,"2013-10-16 13:20:18.993038+01")
  5 | ["2013-10-16 13:21:14.208279+01",infinity)
(4 rows)

Changing the *_inf(period) IS FALSE checks to TRUE rejects valid dates.

Range functions in the manual

Thoughts?