Arbitrating and multiplexing circuitry 28 comprises arbitrating tree circuitry having X arbitrating levels and multiplexing tree circuitry having Y multiplexing levels. The Y multiplexing levels comprise a first set of multiplexing levels upstream of a second set of multiplexing levels. The first set of multiplexing levels operate in parallel with at least some of the arbitrating levels. The second set of multiplexing levels operate in series with the X arbitrating levels such that the second set of multiplexing levels completes the required selection to provide the final output following completion of, and in dependence upon, the arbitration by the arbitrating tree circuitry.