We investigate the mechanisms for the reduction of losses in doped semiconductor multilayers used for the construction of uniaxial metamaterials and show that maximizing the mean scattering time of the doped layers is key to spectrally isolating losses and maximizing anisotropy. By adjusting the layer thickness ratio of the multilayer, we show that the spectral regions of extreme anisotropy can be separated from those of high loss. Using these insights and coupled with realistic semiconductor growth parameters, we demonstrate an InAs-based superlens with an excellent loss factor α ≈ 52mm-1 and maximum perpendicular permittivity, ∊⊥ > 250. By tuning the doping concentration, we show that such a system can be designed to operate anywhere in the region λ0 ≈ 5 to 25μm. We find that such a structure is capable of deep sub-wavelength imaging (< λ0/15) at superlens thicknesses up to ̃85μm (̃8λ0).