This would be after they have had a chance to see their mistakes and would hopefully improve. I would also eliminate the scantron the second time and see if that helped. The advice I would give Gordon is to get rid of the scantron to start with. Maybe have test were you can actual see where the student is having trouble. I find it easier to isolate problems this way instead of multiple choice methods.
Students tend to work a little harder studying especially if it is for partial credit.
At least my kids do. Retest aren't bad. They may respect you a lot more for giving them a second chance. Just don't let them abuse it.