Pipelining allows processors to exploit parallelism. Unfortunately, critical loops -- pieces of logic that must evaluate in a single cycle to meet IPC (Instructions Per Cycle) goals -- prevent deeper pipelining. In today's processors, one of these loops is the instruction scheduling (wakeup and select) logic. This paper describes a technique that pipelines this loop by breaking it into two smaller loops: a critical, single-cycle loop for wakeup; and a non-critical, potentially multi-cycle, loop for select. For the 12 SPECint2000 benchmarks, a machine with two-cycle select logic (i.e., three-cycle scheduling logic) using this technique has an average IPC 15% greater than a machine with three-cycle pipelined conventional scheduling logic, and an IPC within 3% of a machine of the same pipeline depth and one-cycle (ideal) scheduling logic. Since select accounts for more than half the scheduling latency, this technique could significantly increase clock frequency while having minimal impact on IPC.