The depth of a modular invariant ring is a measure of its structural complexity. It is bounded above by Krull dimension, with the two being equal if and only if the ring is Cohen-Macaulay. There is also a lower bound for depth, originally due to Ellingsrud and Skjelbred and later strengthened by Fleischmann, Kemper and Shank. In this talk we will discuss representations for which the lower bound is attained, as well as giving necessary and sufficient conditions for its attainment.