An iterative procedure for optimally estimating the phase angle of a sinusoid of known frequency is presented. The sinusoid is observed in additive Gaussian noise, and the phase angle is assumed to be a Gaussian random variable. The maximum {\em a posteriori} probability (MAP) criterion is used. It is also shown how other signal parameters, such as amplitude and frequency, can be optimally estimated and tracked. Examples are given in which these techniques are used to perform optimum demodulation of angle-modulated signals. The results should dispel the commonly held belief that the best one can do in approaching optimum demodulation of angle-modulated signals is to use a phase-locked loop.