The expectation-maximization (EM) algorithm is a robust method for maximum likelihood estimation of the parameters of an incompletely sampled distribution. It has been used to resolve the trial-to-trial amplitude fluctuations of postsynaptic potentials, when these are recorded in the presence of noise. Its use has however been limited by the need for different recursion equations for each set of conditions defined by the signal and noise processes. These equations are derived for the following conditions which arise in studies of synaptic transmission: non-gaussian noise process; quantal fluctuation; quantal variability. In addition, a constraint can be incorporated to accommodate simple and compound binomial models of transmitter release. Some advantages of these methods are illustrated by Monte Carlo simulations.