Arbitrating and multiplexing circuitry for performing an arbitration between a plurality of inputs and a selection of at least one of said plurality of inputs to provide an output comprises arbitrating tree circuitry having X arbitrating levels, where X is an integer greater than one; and multiplexing tree circuitry having Y multiplexing levels, where Y is an integer greater than one; wherein (i) said Y multiplexing levels comprise a first set of said multiplexing levels upstream of a second set of said multiplexing levels; (ii) said first set of said multiplexing levels is configured to operate in parallel with at least some of said X arbitrating levels, whereby said first set of multiplexing levels is configured to perform a partial selection in parallel with said arbitration performed by said X arbitrating levels; and (iii) said second set of said multiplexing levels is configured to operate in series with said X arbitrating levels, whereby said second set of multiplexing levels completes said selection to provide said output following completion of and in dependence upon said arbitration.