This paper considers the importance of model parameterization, including dispersion, source kinematics, and source discretization, in tsunami source inversion. We implement single and multiple time window methods for dispersive and nondispersive wave propagation to estimate source models for the tsunami generated by the 2011 Tohoku-Oki earthquake. Our source model is described by sea surface displacement instead of fault slip, since sea surface displacement accounts for various tsunami generation mechanisms in addition to fault slip. The results show that tsunami source models can strongly depend on such model choices, particularly when high-quality, open-ocean tsunami waveform data are available. We carry out several synthetic inversion tests to validate the method and assess the impact of parameterization including dispersion and variable rupture velocity in data predictions on the inversion results. Although each of these effects has been considered separately in previous studies, we show that it is important to consider them together in order to obtain more meaningful inversion results. Our results suggest that the discretization of the source, the use of dispersive waves, and accounting for source kinematics are all important factors in tsunami source inversion of large events such as the Tohoku-Oki earthquake, particularly when an extensive set of high-quality tsunami waveform recordings are available. For the Tohoku event, a dispersive model with variable rupture velocity results in a profound improvement in waveform fits that justify the higher source complexity and provide a more realistic source model.