The Super Dual Auroral Radar Network (SuperDARN) is a worldwide chain of HF radars which monitor plasma dynamics in the ionosphere. Autocorrelation functions are routinely calculated from the radar returns and applied to estimate Doppler velocity, spectral width, and backscatter power. This fitting has traditionally been performed by a routine called FITACF. This routine initiates a fitting by selecting a subset of valid phase measurements and then empirically adjusting for 2π phase ambiguities. The slope of the phase variation with lag time then provides Doppler velocity. Doppler spectral width is found by an independent fitting of the decay of power to an assumed exponential or Gaussian function. In this paper, we use simulated data to assess the performance of FITACF, as well as two other newer fitting techniques, named FITEX2 and LMFIT. The key new feature of FITEX2 is that phase models are compared in a least-squares fitting sense with the actual data phases to determine the best fit, eliminating some ambiguities which are present in FITACF. The key new feature of LMFIT is that the complex autocorrelation function (ACF) itself is fit, and Doppler velocity, spectral width, and backscatter power are solved simultaneously. We discuss some of the issues that negatively impact FITACF and find that of the algorithms tested, LMFIT provides the best overall performance in fitting the SuperDARN ACFs. The techniques and the data simulator are applicable to other radar systems that utilize multipulse sequences to make simultaneous range and velocity determinations under aliasing conditions.