Three-dimensional models of the uplift of Beta Regio caused by a mantle plume satisfy constraints on gravity, topography, rheology, and the uplift rate substantially better than two-dimensional models. In particular, the uplift time of Beta Regio is reduced to an acceptable 800 million years. Three-dimensional models give the plume formation depth around 3000 km, which approximately corresponds to the core-mantle boundary. The results depend only weakly on the initial lithospheric thickness (at the time of global resurfacing), including a very thin initial lithosphere. This implies that the thick present-day lithosphere (~400 km) suggested by our models can be reconciled with a thin lithosphere (100--200 km) inferred from the melt generation rates and the flexural rigidity models.