Apparatus and methods for estimating the frequency of a sleep or slow clock by selectively utilizing an estimated sleep clock frequency and an estimated change in the sleep clock frequency. The disclosed apparatus includes a sleep clock frequency estimator to output a fast clock derived sleep clock frequency estimate and a sleep clock change frequency estimator to output an estimate of a change in frequency of the sleep clock. The apparatus further includes a combiner that weights at least one of the fast clock derived sleep clock frequency estimate to obtain a weighted sleep clock frequency estimate and the estimate of the change in frequency of the sleep clock to obtain a weighted estimate of the change in frequency of the sleep clock. The combiner also determines a new estimate of the sleep clock frequency using at least one of the weighted sleep clock frequency estimate and the weighted estimate of the change in frequency of the sleep clock. Complementary methods are also disclosed.