A method of time synchronisation has recently been developed for handling the combination of multipath propagation and fading experienced over HF radio links. The received demodulated signal is sampled here at a rate close to the Nyquist rate. The phase of the sampling instants does not critically affect the performance of the system, as long as it does not vary too rapidly with time; thus it is only necessary to control the sampling rate. Computer-simulation tests have been carried out with the given system on a 9600 bit/s serial data-transmission system. A 16-level QAM signal was transmitted over a model of an HF radio link, with two independent Rayleigh-fading sky waves, and satisfactory time synchronisation was achieved. Unfortunately it has been found that, under very severe fading conditions with three independent Rayleigh-fading sky waves, satisfactory operation is not always obtained with the time synchronisation algorithm. The paper describes various modifications that have been developed for improving the performance of the algorithm, one of these being a fundamental change in the algorithm itself. The paper then presents the results of computersimulation tests, comparing the performances of the original and modified algorithms, and uses these results to determine the most promising system.