Arterial wave speed estimated invasively from pressure (P) and velocity (U) measurements using the P-U loop method, or non-invasively from diameter (D) and U measurements using the lnD-U loop method, assume that during early systole 1) backward-running waves are absent and 2) wave speed is constant. These assumptions also form the basis of a method for correcting time lags between P (or lnD) and U in which the R(2) of the early-systolic linear regression is maximized. However, neither of the two assumptions are strictly valid in vivo, where the diastolic pressure decay from the previous beat may give rise to some non-zero backward-running P, U and wave intensity (WI) components, and the pressure-dependency of wave speed may lead to curvilinearity in the early-systolic P-U and lnD-U relations. Accordingly, this study assessed the robustness of three phase correction algorithms, (including two that are not dependent on the two assumptions stated above, i.e., aligning the times of the peak 2nd derivative or peak signal curvature) and of the P-U and lnD-U loop wave speed estimation methods under a range of diastolic decay rates and degrees of vessel wall non-linearity. Results from a simple computer model of the arterial circulation suggested that although an apparent phase lag may be introduced by assuming linearity, the magnitude of this phase lag is likely to be small considering the sample intervals normally used in experimental studies; however, under highly non-linear flow conditions, the apparent lag may be comparable to hardware-related lags. Predicted errors in estimated wave speed using the P-U loop method were generally less than 10%, while somewhat higher errors were found in the lnD-U loop method (up to 15-20%). In both, higher diastolic pressure decay rates were associated with higher wave speed errors, although this effect was eliminated by subtracting the extrapolated diastolic pressure curve from the measured pressure. Overall, each of the time lag correction algorithms and wave speed estimation methods were generally satisfactory, although further experimental work is required to assess the curvature-based phase correction method and pressure adjustment in vivo.