A new, scalable concept for diode-pumped high-power solid-state lasers is presented. The basic idea of our approach is a very thin laser crystal disc with one face mounted on a heat sink. This allows very high pump power densities without high temperature rises within the crystal. Together with a flat-top pump-beam profile this geometry leads to an almost homogeneous and one-dimensional heat flux perpendicular to the surface. This design dramatically reduces thermal distortions compared to conventional cooling schemes and is particularly suited for quasi-three-level systems which need high pump power densities. Starting from the results obtained with a Ti:Sapphire-pumped Yb:YAG laser at various temperatures, the design was proved by operating a diode-pumped Yb:YAG laser with an output power of 4.4 W and a maximum slope efficiency of 68%. From these first results we predict an exctracted cw power of 100 W at 300 K (140 W at 200 K) with high beam quality from a single longitudinally pumped Yb: YAG crystal with an active volume of 2 mm3. Compact diode-pumped solid-state lasers in the kilowatt range seem to be possible by increasing the pump-beam diameter and/or by using several crystal discs.