Post Search Results Chronologically & Alphabetically.

In my site my members can search for posts by using the search box, which brings up the posts chronologically (which is what I want). My members can also search posts by calendar day (date up loaded) with my ajax calendar. I would like to have the results of the calendar search appear alphabetically. Can I set wordpress to do this or is it a one or the other situation?

Thank you for any help you can provide.