We consider the problem of designing a financial instrument aimed at mitigating the joint exposure of energy-linked commitments to random price and volume delivery fluctuations. We formulate a functional optimization problem over a set of regular payoff functions: one is written on energy price, while the other is issued over any index exhibiting statistical correlation to volumetric load. On theoretical grounds, we derive closed-form expressions for both payoff structures under suitable conditions about the statistical properties of the underlying variables; we pursue analytical computations in the context of a lognormal market model and deliver explicit formulas for the optimal derivative instruments. On practical grounds, we first develop a comparative analysis of model output through simulation experiments; next, we perform an empirical study based on data quoted at EPEX SPOT power market. Our results suggest that combined price-volume hedging performance improves along with an increase of the correlation between load and index values. This outcome paves the way for a new class of effective strategies for managing volumetric risk upon extreme temperature waves.