New techniques for reducing the depth of circuits for cryptographic applications are described. These techniques also keep the number of gates quite small. The result, when applied to the AES S-Box, is a circuit with depth 16 and only 128 gates. For the inverse, it is also depth 16 and has only 127 gates. There is a shared middle part, common to both the S-Box and its inverse, consisting of 63 gates. The best previous comparable design for the AES S-Box has depth 22 and size 148 [Nogami, Nekado, Toyota, Hongo, Morikawa, 2010].