The energy storage market is growing exponentially and residential batteries are being deployed including in grid-connected housing, in order to increase on-site use of PV electricity, i.e. PV self-consumption. However, residential batteries have not reached economic profitability yet in most grid-connected situations, and alternative applications for residential batteries should be explored. This paper presents results from an economic optimization of the operation of a residential battery for two different applications, namely PV self-consumption and demand-load shifting under different dynamic tariff structures. A genetic algorithm was used to identify the optimal operation of the battery for both applications separately as well as combined, in order to investigate whether and under what circumstances the delivery of these two services can help to create an economic case. We find that the greatest monetary value per kWh of storage capacity installed is obtained when a battery is used for PV self-consumption under a single, flat tariff. Furthermore, adding demand-load shifting to the value proposition is economically attractive since it helps to minimize the levelized cost associated with battery storage. We also identify improvements needed for residential batteries to reach economic viability in Switzerland for both PV self-consumption and demand-load shifting, as for example, halving of capital expenditure of the battery system.