Impeachment cross-examination helps to build your case theory only in a negative way, by eliminating competition from the opposition’s theory. As we have previously noted, a cross that reveals that the witness’s testimony is essentially nonsense is one way to impeach.
If you can demonstrate that the witness is saying something illogical, you have gone a long way toward impeaching the witness. In a horrific domestic violence case tried a few years ago, a man claimed that his wife had received her injuries by jumping from a moving car. He explained that she had been high on drugs and acting out in bizarre fashion for the past two weeks. The problem with his story, which was pointed out quite well on cross examination, was that he and his wife had just the previous night arrived in Florida on a commercial flight from Nevada. One fertile area of cross examination proved to be a line of questions on how his severely drug impaired wife got through the TSA screening to get on the plane. The defendant also had some difficulty explaining why, after his wife jumped from the moving car, he took her home, hogtied her, and stuffed her in a closet rather than taking her to the emergency room.