SQL & PL/SQL :: Unique Null And Multiple Non-null

create table test
(
id int ,
dat date
)
/

I want to implement a business rule such as we have for each id at most 1 dat null. So, I've created this unique index on test.

create unique index x_only_one_dat_cess_null on test(id, case when dat_cess is null then 'NULL' else to_char(dat_cess, 'dd/mm/yyyy') end);

insert into test values (1, sysdate);
insert into test values (1, sysdate - 1);
insert into test values (1, null);
insert into test values (1, null);
-- -----
insert into test values (2, sysdate);
insert into test values (2, sysdate - 1);
insert into test values (2, null);

The 4th insert will cause an error and this is what I wanted to implement. OK. Now the problem is that for non-null values of dat, we can't have data like this

iddat
------------
124/10/2013
123/10/2013
123/10/2013
1

because of the unique index (the 2nd and the 3rd row are equal). So just for learning purposes, how could we allow at most one null value of dat and allow duplicates for non-null values of dat.