The probabilistic multihypothesis tracker (PMHT) is a target tracking algorithm of considerable theoretical elegance. In practice, its performance turns out to be at best similar to that of the probabilistic data association filter (PDAF); and since the implementation of the PDAF is less intense numerically the PMHT has been having a hard time finding acceptance. The PMHT's problems of nonadaptivity, narcissism, and over-hospitality to clutter are elicited in this work. The PMHT's main selling-point is its flexible and easily modifiable model, which we use to develop the "homothetic" PMHT; maneuver-based PMHTs, including those with separate and joint homothetic measurement models; a modified PMHT whose measurement/target association model is more similar to that of the PDAF; and PMHTs with eccentric and/or estimated measurement models. Ideally, "bottom line" would be a version of the PMHT with clear advantages over existing trackers. If the goal is of an accurate (in terms of mean square error (MSE)) track, then there are a number of versions for which this is available.