In 2013, Reeder–Yu gave a construction of supercuspidal representations by starting with stable characters coming from the shallowest depth of the Moy–Prasad filtration. In this talk, we will be diving deeper—but not too deep. In doing so, we will construct examples of supercuspidal representations coming from a larger class of “shallow” characters. Using methods similar to Reeder–Yu, we can begin to make predictions about the Langlands parameters for these representations.