The Müller Ice Cap will soon set the scene for a new drilling project. Therefore, ice thickness estimates are necessary for planning, since thickness measurements of the ice cap are sparse. Here, three models are presented and compared: (i) a simple Semi-Empirical Ice Thickness Model (SEITMo) based on an inversion of the shallow-ice approximation by the use of a single radar line in combination with the glacier outline, surface slope, and elevation; (ii) an iterative inverse method using the Parallel Ice Sheet Model (PISM), and (iii) a velocity-based inversion of the shallow-ice approximation. The velocity-based inversion underestimates the ice thickness at the ice cap top, making the model less useful to aid in drill site selection, whereas PISM and the SEITMo mostly agree about a good drill site candidate. However, the new SEITMo is insensitive to mass balance, computationally fast, and provides as good fits as PISM.