How to avoid X'es around point sources in maximum likelihood CMB maps

The maximum likelihood estimator for CMB map-making is optimal and unbiased as long as the data model is correct, but in practice it rarely is, with model errors including sub-pixel structure and instrumental problems like time-variable gain and pointing errors. In the presence of such errors, the solution is biased, with the local error in each pixel leaking outwards along the scanning pattern by a noise correlation length. The most important sources of such leakage are strong point sources, and for common scanning patterns the leakage manifests as an X around each such source. I discuss why this happens, and present several old and new methods for mitigating and/or eliminating this leakage, along with a small stand-alone TOD simulator and map-maker in Python that implements them.