This study considers application-oriented models of lithium-sulfur (Li-S) cells. Existing ECN models often neglect self-discharge, but this can be important in applications. After describing the context in which control-oriented models and estimators are based, the self-discharge phenomenon is investigated for a new 21 Ah Li-S cell. As a contribution of this study, an equivalent-circuit-network (ECN) model was extended to account for cells' self-discharge. Formal system identification techniques were used to parameterize a model from experimental data. The original model was then extended by adding terms to represent a self-discharge resistance. To obtain the self-discharge resistance, a particular new series of experiments were designed and performed on the Li-S cell at various temperature and initial state-of-charge (SoC) levels. The results demonstrate the dependency of self-discharge rate on the SoC and temperature. The self-discharge rate is much higher at high SoC levels and it increases as temperature decreases. (C) The Author(s) 2017. Published by ECS.