Seriously consider your options for going to a full 2GB of RAM if you can--at least here the difference between 1GB and 2GB is not more than fifty bucks or so, and it'll buy you a whole lot more than fifty bucks' worth of satisfaction!
While plenty of people are running Zimbra on less, 2GB seems to be a sweet spot at which even very small installations (and I mean small like test beds of a couple of users) start running MUCH faster and more smoothly.
Cheers,
Dan