Single-point methods such as the PU- and QA-loop methods are used to estimate local pulse wave velocity (PWV-PU and PWV-QA) in arteries from a combination of pressure (P), flow (Q), velocity (U) or cross-sectional area (A) waveforms. Available data indicate that the PU-loop method tends to overestimate PWV, while the QA-loop method tends to underestimate. Wave reflection has been suggested as a factor playing a role in the agreement between different methods. In this work, we (i) demonstrate the interference of wave reflection with the PU-loop method for both solitary sinusoidal waves as well as physiological waveforms; (ii) develop an operator-independent method to correct for the presence of reflections. Fluid-structure interaction simulations in a tube and carotid artery model with known mechanical properties confirm the theory. For the carotid artery model, PWV-PU severely overestimates PWV, while PWV-QA underestimates PWV. Correction (leading to an estimate termed PWV-corr) eliminates the impact of reflections. Finally, methods are applied in vivo in a subsample of the Asklepios population. Compared to PWV-PU and PWV-QA, PWV-corr leads to significantly better correlations of carotid PWV with PWV derived from carotid distensibility based on the Bramwell-Hill equation(with r² improving from about 0.25 to 0.91). Neither the PU-loop nor the QA-loop method provides reliable estimates of local PWV in settings where wave reflections are present - even when the PU- or QA-loops show a linear segment. They offer no alternative for the Bramwell-Hill based approach and their application should therefore be discouraged, especially for the carotid artery.