I know here in Charleston, if you are zoned for a school that has consistently performed at "below average" or "unsatisfactory" for a number of years, you can apply to attend a better performing school.
With the timeline for this transfer request, you actually start the year at the lowering perfomring school. Around October, or whenever the previous year's PACT scores come out, the transfer applications come out on the District's web site.
I am not sure how this would affect elegibility for spring sports though. Also, if your new school falls below "average" the following year or does not meet AYP, you get sent back to the school you are zoned for.