In this situation I tend to follow the Montgomery Scott Miracle Worker Rule(tm). Come up with a nice, comfortable number in your head, pad it out a little if necessary so it's a nice round number, then multiply by 4.
The only thing that worries me with this technique (as tempting as it is), is that I've seen teams where the work will dramatically slow down because they're trying to "fit" to the deadline. Getting it done as fast as possible and early only leads to more work for more people.
