The cross-examination period of a debate is a time when the person who is not going to speak next in the constructives questions the person who has just finished speaking. Consider cross examination an information exchange period - it is not the time to role play lawyer.
Most debaters tend to ignore the value of good cross-examination.
If nothing else, debaters tend to underestimate the importance that cross-examination may have on the judge. In cross-examination, briefs are not read and advanced arguments are not spewed out. Cross-examination will indicate to the judge just how sharp and spontaneous the debaters are. Invisible bias will always occur in a debate round and judges would always like the sharpest team to win. Good, effective cross-examination of the opponents can play an important psychological role in winning the ballot of the judge.