Triggers

I have a with a a column defined as not null. The value however can be
found by looking it up in another table. I would like to create a
trigger that after insert would look up the need value and put it in the
record being inserted.

Unfortunately the column is defined as not null so I fear the insert
would fail and the trigger never get called. How can I get around this?

i.e.

create table t {

id serial primary key,
a integer not null,
b integer not null -- b can be found in another table
};

insert into t(a) values('1'); -- this would start the trigger and turn
the insert into:

insert into t(a,b) values('1', 'some value from another table');

Are thriggers the wrong way to go about this?

Jc