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Energy-parity objectives combine ω-regular with quantitative objectives of reward MDPs. The controller needs to avoid to run out of energy while satisfying a parity objective. We refute the common belief that, if an energy-parity objective holds almost-surely, then this can be realised by some finite memory strategy. We provide a surprisingly simple counterexample that only uses coBüchi conditions. We introduce the new class of bounded (energy) storage objectives that, when combined with paritydoi:10.1109/lics.2017.8005131 dblp:conf/lics/MayrSTW17 fatcat:2cap4uknx5bdzbeqqe6q6tbcfq