Carrier frequency estimation plays an important role in digital communication receivers. A progressive refinement approach to maximum-likelihood estimation is proposed as a means to improve the performance of a suboptimal estimation algorithm and achieve different tradeoffs among complexity, accuracy and dynamic range. As an example, an application is described for carrier frequency recovery in burst-mode digital transmissions. The Luise and Reggiannini (1995) synchronization algorithm is employed as the master frequency estimator. The performance of the algorithm is demonstrated by means of a simulation study, assuming quadrature phase-shift keying modulation; the results show that the progressive refinement approach can be usefully exploited, for example to improve the estimation range of the LR algorithm, without losing the accuracy and the computational complexity.