The design uses a composite Yb:YAG/YAG disc laser configuration with the pump light incident from the disc edge. The crucial advantages of the thin-disc design is that the thermal gradients are aligned with the beam propagation direction, the transverse temperature gradients are reduced, previous difficulties with high average power pumping/cooling and the rejection of amplified spontaneous emission are resolved. In contrast to high power rods or slabs, the one-dimensional nature of the cooling geometry and the edge-pump geometry scale gracefully to very high average power. Two point designs illustrating power scaling are also given as examples.