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The mixed Lp-norm, 0 ≤ p ≤ 2, stabilization algorithm is flexible for constructing a suite of subsurface models with either distinct, or a combination of, smooth, sparse, or blocky structures. This general purpose algorithm can be used for the inversion of data from regions with different subsurface characteristics. Model interpretation is improved by simulta- neous inversion of multiple data sets using a joint inversion approach. An effective and general algorithm is presented for the mixed Lp-norm joint inversion of gravity and magnetic data sets. The imposition of the structural cross-gradient enforces similarity between the reconstructed models. For efficiency the implementation relies on three crucial realistic details; (i) the data are assumed to be on a uniform grid providing sensitivity matrices that decompose in block Toeplitz Toeplitz block form for each depth layer of the model domain and yield efficiency in storage and computation via 2D fast Fourier transforms; (ii) matrix-free implementation for calculating derivatives of parameters reduces memory and computational overhead; and (iii) an alternating updating algorithm is employed. Balancing of the data misfit terms is imposed to assure that the gravity and magnetic data sets are fit with respect to their individual noise levels without overfitting of either model. Strategies to find all weighting parameters within the objective function are described. The algorithm is validated on two synthetic but complicated models. It is applied to invert gravity and magnetic data acquired over two kimberlite pipes in Botswana, producing models that are in good agreement with borehole information available in the survey area.