Magnetotelluric (MT) problems often contain different subdomains where the conductivity of the media depends upon one, two, or three spatial variables. Traditionally, when a MT problem incorporates a three-dimensional (3D) subdomain, the numerical method employed for simulation and inversion was 3D over then entire domain. In here, we propose to take advantage of the possibly lower dimensionality of certain subdomains during the inversion process. By doing so, we obtain significant computational savings (up to 75% in some scenarios) and increased accuracy on the results. We numerically illustrate this method by employing two dimensional (2D) computations based on a multi-goal oriented . hp-adaptive Finite Element Method (FEM) that exhibits superior convergence properties. Additionally, we provide a formulation for implementing an efficient adjoint based method for the computation of the derivatives of the impedance, and we show the importance of the (a) proper selection of the inversion variable, and (b) the advantages of using both the Transverse Electric (TE) and Transverse Magnetic (TM) measurements for the proper inversion of MT data.