Actually, randomness might be better. I'd suggest having a pool of 36 or 48 jurors in six or eight randomly-drawn groups of six. Each side's lawyer gets to strike two/three of the six/eight groups for any reason or no reason, but does not get to pick and choose.
BTW, one thing I was wondering about awhile ago: what happens or should happen if, during a case, a juror becomes aware of something that might impair his impartiality, but which he could not have known before the case?
As a hypothetical example, suppose that during a trial, a jury recognized one of the defendant's character witnesses as a shoplifter he'd observed in the act but failed to aprehend? Unless the jury was shown photos of all the witnesses before the trial (which I don't think is generally the case) there would be no way for the juror to know of the issue beforehand, but the juror's knowledge about the witness would preclude a fair and impartial evaluation of his testimony. What would be the legally correct and proper thing for the juror to do in such a case?
Such jurors are supposed to recuse themselves and be replaced by the already empaneled alternates.
Heh. You just described how jury selection works now, almost exactly. Only the numbers are different. The no-questions-asked strikes are called "peremptory challenges." You can also get a juror stricken if there's a compelling reason: this is called "challenge for cause."