In Hallett v. Houston Northwest Medical Center, 689 S.W.2d 888, 890 (Tex. 1985), the Texas Supreme Court explained the procedure to preserve a complaint for appeal in situations involving a trial court's refusal to grant a party's request for additional peremptory strikes.
The Hallett Court stated, that to preserve error, a party, prior to exercising its peremptory challenges, must "advise the trial court of two things:
(1) that she would exhaust her peremptory challenges; and;
(2) that after exercising her peremptory challenges, specific objectionable jurors would remain on the jury list." Id. at 890.