This contribution deals with estimation and compensation of phase noise in single-carrier digital communications. We present an iterative feedforward decision-directed phase noise estimation algorithm, that is based on approximating the phase noise process by an expansion of DCT basis functions containing only a few terms. An extension to the estimation algorithm is proposed, improving the performance in terms of the mean-square error. We demonstrate that the resulting (linearized) mean-square estimation error consists of two contributions: a contribution from the additive noise, that equals the Cramer-Rao lower bound, and a noise-independent contribution that results from the phase noise modeling error. The phase estimate that yields the lowest possible mean-square error is obtained, assuming knowledge of the phase noise statistics at the receiver.