A WSN consists of numerous nodes gathering observations and combining these observations. Often, the timing of these observations is of importance when processing sensor data. Thus, a need for clock synchronization arises in WSNs. The CS-MNS algorithm has been proposed to fulfil this role. However, the core algorithm suffers from an initial divergence of clocks. This paper shows, through analysis, that introducing a bias factor in the CS-MNS update law significantly reduces this initial divergence. This is then further confirmed via simulation results, using Matlab, and actual testbed measurements in a testbed deploying motes running TinyOS 2.1. The results show that a designer, having some a-priori knowledge about clock characteristics, can choose a bias that allows the algorithm to speed up the convergence time and greately improve the overall protocol performance. The work also demonstrates that rigorous analysis can be helpful in designing protocols and predicting protocol behaviour, which is then verified through simulation and testbed measurements.