We optimize the effective skin-depth and resolution of Ag-TiO2, Ag-SrTiO3, and Ag-GaP multilayers for imaging with sub-wavelength resolution. In terms of transmission and resolution, the optimized multilayers outperform simple designs based on combined use of effective medium theory, impedance matching and Fabry–Perot resonances. For instance, an optimized Ag-GaP multilayer consisting of only 17 layers, operating at the wavelength of 490 nm and having a total thickness equal to one wavelength, combines 78% intensity transmission with a resolution of 60 nm. It is also shown that use of the effective medium theory leads to sub-optimal multilayer designs with respect to the trade-off between the skin depth and resolution already when the period of the structure is on the order of 40 nm or larger.