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An acoustic couplant layer plays an integral role in many ultrasonic nondestructive testing and material characterization applications. It is important to account for this layer for accurate time-delay measurements. In pulse-echo measurements, the couplant layer can be accounted for by modeling the frequency dependence of phase delay. In this paper, two such models are evaluated for robustness in determining an accurate phase velocity: a simple linear relationship and the acoustic transmission line with its associated nonlinear expression. For this evaluation, measurements of acoustic phase delay in an aluminum sample were made by the pulse-echo method using tone bursts of 1800 different carrier frequencies between 35 and 125 MHz. The transmission line model was fit to the measured data using an unconstrained nonlinear least squares fitting routine with two free parameters: the acoustic phase velocity in the sample and the couplant thickness. It was found that this nonlinear model was extremely sensitive to the initial parameter guesses and could not unambiguously determine both the couplant layer thickness and acoustic phase velocity. In contrast, the faster and simpler linear least squares fit to the delay data determines a unique phase velocity in agreement with resonant ultrasound spectroscopy, an independent measurement technique.