We present a new geometry for edge-pumping of a solid-state microchip laser. This design, which consists of a thin-disk gain crystal that has on top a diffusion bonded undoped material that guides the pump light, allows a good thermal heat management by reducing the thickness of the gain media, whereas the pump optics is kept simple. Simulations show that more than 0.95 of the pump radiation with uniformity coefficient in excess of 0.95 can be absorbed in an Yb:YAG/YAG composite device that has a 200-mum thick, 15-at.% Yb:YAG of 3.6-mm diameter. First experiments with this configuration produced on-time 34 W output power for 220 W on-time pump power and 0.26 slope efficiency. Power scaling possibilities are discussed.