We consider the problem of estimating the frequency offset between the transmitter and receiver in flat-fading communication channels using a training sequence. Kuo and Fitz (1997) and Morelli, Mengali and Vitetta (see IEEE Commun. Lett., vol.2, p.327-30, 1998), proposed two frequency estimators to solve the aforementioned problem. They rely on weighted linear regression for the phases of the correlation sequence or their differences. The method of Kuo et al. needs phase unwrapping and both methods require knowledge of the correlation of the fading process. In this paper, two simple methods which do not require any of these assumptions are proposed. The first is the unweighted version of the method of Morelli et al. The second is drawn from the array processing framework. It is based on a nonlinear least-squares approach that assumes an unstructured correlation of the fading process. The performance of the proposed methods is as good as that of the methods of Kuo et al. and Morelli et al., but the robustness of our methods to modeling errors is much enhanced.