After a review of the development of the Mayne-Fraser two-filter smoother, a first principle argument is used to rederive this smoother. Reversed-time Markov models play a key role in forming a state estimate from future observations. The built-in asymmetry of the Mayne-Fraser smoother is pointed out, and it is shown how this asymmetry may be removed. Additionally, a covariance analysis of the two-filter smoother is provided, and reduced-order smoothers are analyzed.