We present a method of identifying bright sources of ultra-high energy cosmic rays (UHECRs) embedded in a diffuse background flux by studying UHECR arrival directions. The technique is applicable to sources that produce several observed events, which exhibit energy ordering in their arrival directions due to coherent deflections caused by the regular component of the Galactic magnetic field. We quantify the efficiency of the method with numerical simulations which take into account the possible uncorrelated values of the extragalactic magnetic fields that the UHECRs might encounter, possible turbulent magnetic fields in our own Galaxy, and in particular the non-uniform exposure of UHECR observatories. In the absence of energy ordering in excess of background expectations we place an upper limit on the flux fraction contributed by the brightest UHECR source, which can constrain models of the origin of UHECRs and their composition.