At least one instruction storage coupled with a fetch unit including sets of fetch circuitry each having a same plurality of pipeline stages. The sets of fetch circuitry perform fetch operations to fetch blocks of instructions from the at least one instruction storage. Stall circuitry, in response to an indication of a hazard for a given pipeline stage of a first set of fetch circuitry, retains a fetch operation for a first block of instructions at the given pipeline stage, and zero or more fetch operations for zero or more corresponding blocks of instructions at zero or more preceding pipeline stages of the first set of fetch circuitry, until the hazard has been removed. The stall circuitry advances a fetch operation for a second block of instructions from the given pipeline stage of a second set of fetch circuitry, during an initial cycle of the one or more cycles.