There is certainly an art to cross-examination, especially in the role of the one being questioned. Nobody likes to be on the hot seat. You are standing at the podium for three straight minutes, questions being hurled at you rapid-fire, and no means of escape are available. I've seen many methods of dealing with this challenge and grew to enjoy it by utilizing what I found as the most successful strategy.
Many veteran debaters pride themselves on their quick, verbal feet in cross-examination. They tap dance around questions lobbed at them by avoiding a real answer, stringing out mumbo jumbo, or always contradicting the opposing speaker. Often, the answering debaters go with the strategy of never agreeing with any question thrown their way.
Yet with this approach, I've seen many speakers caught giving ridiculous answers, denying the obvious, or at least seeming obstinate. As a former debater who now sits at the judges chair, I can tell you this method is unconvincing. I remind my students over and over that debates are simply a contest of credibility. If you appear stubborn, unreasonable, or standoffish, you are losing traction in the debate. After all, the round is determining for the judge who they should trust to best inform them on the issues presented.
The best approach for answering questions in cross-x is to be honest and forthcoming. You don't have to volunteer information damaging to your case, but you should give an honest and complete answer. This strategy not only gives you a better foundation of credibility but it also forces you towards arguments you actually believe you can defend.
There is a place for tap-dancing, but it should be more mental and less verbal. Great debaters know where their opponent is heading with a line of questioning. They counter by giving an honest answer followed by analysis of why it impacts the round for their own side. In this fashion, the debater on the "hot seat" actually can reaffirm their own speech and case despite not having control over the questioning.
In summary, be forthcoming. Provide honest answers. Analyze the line of questioning and show how the arguments still support your assertions. Incorporating these skills into your arsenal will give you the IMPACT of excellence.