How can you generate a counter for ordered sets?

I am in the process of transitioning a bioinformatics database from  
one schema to another, and I have to do some "massaging" of the data  
in order to do it.

I have two tables, "gene" and "exon".  Exon has a many-to-one  
relationship with Gene.  The structure of the Gene table isn't  
important, but the Exon table looks like this:

CREATE TABLE exon(id SERIAL PRIMARY KEY,gene INTEGER REFERENCES gene(id),start INTEGER,stop INTEGER
);

Conceptually, all the exons for a given gene form a set, ordered by  
their "start" attribute.  I need to add a new integer column to the  
table to store a counter for each exon that indicates their position  
in this ordering.

Is there a straightforward way to populate this new position column?   
I've done an iterative solution in PL/pgSQL which works (slowly), but  
I was wondering if there was a more efficient way to do this kind of  
thing.

Thanks in advance,

Christopher Maier