A modification of the typical minimum-structure inversion algorithm is presented that generates blocky, piecewise-constant earth models. Such models are often more consistent with our real or perceived knowledge of the subsurface than the fuzzy, smeared-out models produced by current minimum-structure inversions. The modified algorithm uses -type measures in the measure of model structure instead of the traditional sum-of-squares, or , measure. An iteratively reweighted least-squares procedure is used to deal with the nonlinearity introduced by the non- measure. Also, and of note here, diagonal finite differences are included in the measure of model structure. This enables dipping interfaces to be formed. The modified algorithm retains the benefits of the minimum-structure style of inversion — namely, reliability, robustness, and minimal artifacts in the constructed model. Two examples are given: the 2D inversion of synthetic magnetotelluric data and the 3D inversion of gravity data from the Ovoid deposit, Voisey's Bay, Labrador.