A technique efficiently selects a Path Computation Element (PCE) to compute a path between nodes of a computer network. The PCE selection technique is illustratively based on dynamic advertisements of the PCE's available path computation resources, using (i) a low-pass filter algorithm to compute such resources, and (ii) threshold determinations to control distribution of those advertisements. To that end, the novel technique enables one or more PCEs to dynamically send (advertise) their available path computation resources to a Path Computation Client (PCC) by way of the controlled advertisements. In addition, the technique enables the PCC to efficiently select a PCE (or set of PCEs) to service a path computation request based upon those available resources.