A new class of fast-converging timing recovery methods for synchronous digital data receivers is investigated. Starting with a worst-case timing offset, convergence with random binary data will typically occur within 10-20 symbols. The input signal is sampled at the baud rate; these samples are then processed to derive a suitable control signal to adjust the timing phase. A general method is outlined to obtain near-minimum-variance estimates of the timing offset with respect to a given steady-state sampling criterion. Although we make certain independence assumptions between successive samples and postulate ideal decisions to obtain convenient analytical results, our simulations with a decision-directed reference and baud-to-baud adjustments yield very similar results. Convergence is exponential, and for small loop gains the residual jitter is proportional and convergence time is inversely proportional to the loop gain. The proposed algorithms are simple and economic to implement. They apply to binary or multilevel PAM signals as well as to partial response signals.