When I say "teams of two students", I don't mean "you write the first half of the assignment, and I'll write the second half"; I want both students working together on all of the assignment, using the techniques of Pair Programming: two people using one workstation, with one typing and the other "looking over the first one's shoulder". If you haven't encountered this approach before, I'll point you to a good article about it.
It's hard to define what constitutes "cheating" in this sort of course. Students are encouraged to help one another with mechanical and linguistic difficulties ("how do I save this file?", "how do you declare a static instance variable?", etc.), regardless of whether they're on the same team, but designing, coding, testing, and debugging should be done by team members. It's remarkably easy for a professor to notice when three different teams have turned in nearly-identical programs; if that happens, I'll grade it once and divide the credit among the three, so the best any of them can hope for is 33%.
All work on the final exam must be entirely the work of the one person whose name is at the top of the page. If I have evidence that one student copied from another on an exam, both students will be penalized; see above.