Multisensor-multitarget sensor management is at root a problem in nonlinear control theory. This paper develops a potentially computationally tractable approximation of an earlier (1996) Bayesian control-theoretic foundation for sensor management based on “finite-set statistics” (FISST) and the Bayes recursive filter for the entire multisensor-multitarget system. I analyze possible Bayesian control-theoretic objective functions: Csiszar information-theoretic functionals (which generalize Kullback-Leibler discrimination) and “geometric” functionals. I show that some of these objective functions lead to potentially tractable sensor management algorithms when used in conjunction with MHC (multi-hypothesis correlator)-like algorithms. I also take this opportunity to comment on recent misrepresentations of FISST involving so-called “joint multitarget probabilities (JMP).”.