Selecting next ID and less?

I'm working on a puzzle game, where users must solve many different puzzles. Once they complete a puzzle, they will be able to try the next puzzle. Each puzzle is stored as a row in the puzzle in a database table. The problem is, how would I select the puzzles the next highest puzzle and lower? I could use a query something like "select * from puzzles where id <= $completedid + 1", but it would break is there were any holes in the ID. Also, it would use the ID as something more than a unique identifier for each row, which is a bad thing. Any suggestions for a better way?