Soft wet grounds such as mud, sand, or forest soils are complex to navigate because it is hard to predict the response of the yielding ground and energy lost in deformation. In this paper, we address the control of static quadruped walking in deep mud. We present and compare three controllers with increasing complexity that use a combination of a creeping gait, a footsubstrate interaction detection, and a model-based Center of Mass positioning. We implement and test the controllers on a Go1 quadruped robot and also compare the performance to the commercially available dynamic gait controller of Go1. While the commercially available controller was only sporadically able to traverse in 12cm deep mud with a 0.35 water/solid ratio for a short time, all proposed controllers successfully traversed the testground while using up to 4.25 times less energy. The results of this paper can be used to deploy quadruped robots on soft wet grounds, so far inaccessible to legged robots.