There have been several recent claims of black hole binaries in globular clusters. I show that these candidate systems could instead be ultracompact X-ray binaries (UCXBs) in which a neutron star accretes from a white dwarf. They would represent a slightly earlier evolutionary stage of known globular cluster UCXBs such as 4U 1820-30, with white dwarf masses similar to 0.2 M-circle dot and orbital periods below 5 minutes. Accretion is slightly super-Eddington and makes these systems ultraluminous sources with rather mild beaming factors b similar to 0.3. Their theoretical luminosity function flattens slightly just above L-Edd and then steepens at similar to 3L(Edd). It predicts of order two detections in elliptical galaxies such as NGC 4472, as observed. The very bright X-ray source HLX-1 lies off the plane of its host S0a galaxy. If this is an indication of globular cluster membership, it could conceivably be a more extreme example of a UCXB with white dwarf mass M-2 similar or equal to 0.34 M-circle dot. The beaming here is tighter (b similar to (2.5-9) x 10(-3)), but the system's distance of 95 Mpc easily eliminates any need to invoke improbable alignment of the beam for detection. If its position instead indicates membership of a satellite dwarf galaxy, HLX-1 could have a much higher accretor mass similar to 1000 M-circle dot.