We present an improved estimator of the phase noise theta(t) in OFDM systems, based on the approximation of the timevarying phasor exp(jtheta(t)) by a discrete-cosine transform (DCT) basis expansion, containing only a few terms. Using pilot symbols, an initial least-squares estimate of the phase noise is obtained. The initial estimate is iteratively improved by also exploiting the soft decisions from the data symbols, obtained in a previous iteration. We demonstrate that the resulting (linearized) meansquare estimation error consists of two contributions: a contribution from the additive channel noise, that equals the modified Cramer-Rao lower bound when the soft decisions are assumed to equal the true data symbols, and a contribution that results from the phase noise modeling error. The modified Cramer-Rao lower bound is shown to be proportional to the number of estimated DCT coefficients. Performance can be optimized by a proper selection of the number of DCT coefficients in the expansion of the phasor. Iterative soft-decision-directed phase noise estimation yields a considerable performance improvement as compared to estimation using only pilot symbols. For an OFDM system with strong phase noise, the BER performance degradation resulting from the proposed scheme is limited to about 1 dB only.