It may be somewhat counterintuitive, but the impeachment of a witness is not the primary goal of cross-examination. The primary goal of cross-examination is to persuade the jury to endorse your case theory. Impeaching opposing witnesses contributes to proving your case theory only indirectly. It tends to encourage the finder-of-fact to reject the opposing side’s theory. It is especially true in the realm of criminal prosecution that this rejection of the opposition theory may or may not advance your case theory. If you are the prosecutor and the jury disbelieves your theory, it makes little difference whether they believe the defense theory. Thus, impeachment helps to build your case theory only in a negative way, by eliminating competition from the opposition’s theory.
Impeachment comes in three basic flavors:
1. illogic,
2. incrimination, and
3. inconsistency.

1. Illogic

If you can demonstrate that the witness is saying something nonsensical, 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.

2. Incrimination

Incrimination, of course, means conviction of crime, but we use it here in a broader sense to mean any evidence of bad character. Indeed, in many jurisdictions across the nation impeachment by prior conviction has been so sanitized that it can have little effect on the witness’s credibility. In Florida, for example, the only questions that can be asked are:
Q: Have you ever been convicted of

[a felony] [a crime involving dishonesty or false statement]?
Q: How many times.
It is essential, however, that the witness be prepared to answer the questions. Unless your witness understands the process of impeachment by prior conviction, you just might be embarrassed to hear a colloquy something like this question and answer from a long-ago burglary case:
Q: Have you ever been convicted of a crime?
A: I did time for manslaughter once, but I didn’t kill him. I just stabbed him. He died in the hospital.

3. Inconsistency

Inconsistency is probably the most frequently employed method of impeachment, especially in cases where depositions have been taken. Sometimes the inconsistency is not an internal conflict between what the witness now says and what the witness once said. Sometimes it is a conflict between what the witness says and another witness or some irrefutable fact. A recent example of this type of impeachment was seen in the trial of George Zimmerman. In the early days of the investigation, Zimmerman had gone on a nationally televised talk show and asserted that he had never heard of Florida’s “Stand Your Ground” law (SYG). Given the pervasive coverage of the public debate surrounding the passage of SYG, this assertion was inherently implausible. The prosecution was not content to simply rely on the inherently implausibility, but went on to call a professor who had taught a criminal justice class which Zimmerman had taken in college. The professor thoroughly contradicted Zimmerman by revealing that he had been taught about SYG in the class. This impeachment of Zimmerman tends to validate what we said at the beginning of this post. Impeaching a witness often does very little toward the primary objective of persuading the finder-of-fact to accept your case theory.