The celebrated quantum ergodicity theorem of Shnirelman, Zelditch, and Colin de Verdière established that ergodic dynamical assumptions on a Hamiltonian system are manifested in eigenfunction equidistribution results for the corresponding quantised system. This result has led to questions of converse QE. Can Hamiltonian systems with non-ergodic dynamics exhibit the same eigenfunction equidistribution? In this talk I will present my recent work on establishing the non-quantum ergodicity of a class of KAM Hamiltonian systems. A key ingredient is the use of a construction of highly accurate quasimodes due to Popov. This project is the culmination of my doctoral research under the supervision of Professor Andrew Hassell.