We previously presented a highly accurate, spline-based time delay estimator that directly determines subsample time delay estimates from sampled data. The algorithm uses cubic splines to produce a continuous time representation of a reference signal, and then computes an analytical matching function between this reference and a delayed signal. The location of the minima of this function yields estimates of the time delay. In this paper we present more computationally efficient formulations of this algorithm. We present the results of computer simulations and ultrasound experiments which indicate that the bias and the standard deviation of the proposed algorithms are comparable to those of the original method, and thus superior to other published algorithms.