Maximum-likelihood estimation of phase and frequency offset involves the maximization of a nonlinear likelihood function. We develop an estimator for carrier acquisition by linearizing the likelihood-function, and show that its performance is close to the Cramer-Rao bound (CRB). The estimator is then extended to blind frequency acquisition and combined with testing to eliminate unlikely hypotheses. With proper modeling of the likelihood resulting from the blind search, simulations show that the algorithm quickly rejects all but the correct frequency hypothesis.