At group meeting, Vakili showed his results on star positional measurements. We have several super-fast, approximate schemes that come close to saturating the Cramér–Rao bound, without requiring a good model of the point-spread function.
One of these methods is the (insane) method used in the SDSS pipelines, which was communicated to us in the form of code (since it isn't fully written up anywhere). This method (due to Lupton) is genius, fast, runs on minimal hardware with almost no overhead, and comes close to saturating the bound. Another of these is the method made up on the spot by Price-Whelan and me when we wrote this paper on digitization bandwidth, with a small modification (involving smoothing (gasp!) the image); the APW method is simpler and faster than the SDSS method on modern compute machinery.
Full-up PSF modeling should beat (very slightly) both of these methods, but it degrades in an unknown way as the PSF model gets wrong, and who is confident that he or she has a perfect PSF model? Vakili is going to have a nice paper on all this; we started writing it just as an aside to other things we are doing, but we realized that much of what we are learning is not really in the literature. Let's hear it for the analysis of astronomical engineering infrastructure!