I have only just recently begun experimenting with TBL but in all my classes I have moved individual quizzes/exams/RATs to Blackboard. I used to worry about cheating by doing this but in the past 4-5 years of doing things things way I have seen literally no difference in the overall scores between taking them in-class or electronically. I would like to attribute this to the first question on all my electronic quizzes, etc., which asks students to verify that they aren't cheating (pangs of conscience) but the more likely reason is that my classes tend to have mostly majors and minors who don't want to risk being caught.

By moving to Blackboard I am able to give the students a larger window during which to take the quiz/exam/RAT (usually 24-36 hours) and I can set the timer for each assignment to accommodate the time-and-a-half some test-takers need. I also have the completion time 30-60 minutes before my class begins so that I can review individual responses before tQuizzes/tRATs.