Least-squares (LS) acoustic-waveform inversion often suffers from a very narrow basin of attraction near the global minimum. To mitigate this problem, we evaluated an iterative inversion scheme in which the notion of proximity of two traces is not the usual LS distance, but instead it involves registration as in image processing. Observed data were matched to predicted waveforms via piecewise-polynomial warpings, obtained by solving a nonconvex optimization problem in a multiscale fashion from low to high frequencies. This multiscale process required defining low-frequency augmented signals to seed the frequency sweep at zero frequency. Custom adjoint sources were then defined from the warped waveforms. The new method, referred to as registration-guided least-squares, was successfully applied to a few scenarios of model velocity estimation in the transmission setting. We determined that the new method can converge to the correct model in situations in which conventional LS inversion suffers from cycle skipping and converges to a spurious model.