LetA be any nonrecursive set. We define a hierarchy of sets (and a corresponding hierarchy of degrees) that are reducible toA based on bounding the number of queries toA that an oracle machine can make. WhenA is the halting problemK our hierarchy of sets interleaves with the difference hierarchy on the r.e. sets in a logarithmic way; this follows from a tradeoff between the number of parallel queries and the number of serial queries needed to compute a function with oracleK.