In Ex parte Ybarra, 149 S.W.3d 147 (Tex. Crim. App. 2004), the Court of Criminal Appeals held that the trial court's failure to award all of the defendant's presentence jail time when the court pronounced sentence could be corrected by a judgment nunc pro tunc.
In Ybarra, there was no plea bargain in place, and it was clear from the record that Ybarra was entitled to the amount of back-time that the statute provided.
An incorrect calculation of the amount of back-time awarded to a defendant, or the omission of any statutory back-time in the judgment can be adjusted by a motion for judgment nunc pro tunc.