Our "magnet" school is pretty much what Blackcat described. Ours started as few years ago as a response to our district losing students to the adjoining district's gifted program, which identifies kids at 1st grade and to local private schools.
Some of the privates have started a "PACE" program to allow for acceleration by making all core classes start at the same time over grade levels, in response to parents pulling them out to apply at our school.