The demand/supply balance in a power grid faces great challenges as more and more renewables are integrated into the system. Fluctuations in the power supply increases spectacularly owing to the uncertain nature of renewables. In this case, it has been widely recognized that the conventional scheme of supply following load is neither economically efficient nor environmentally friendly. On the contrary, an alternative paradigm has been attracting more and more attention over the recent years which attempts to utilize the flexibilities in the demand side to compensate the uncertainties in the supply side. Following this direction, we propose a duration-deadline jointly differentiated energy service in this paper. Specifically, we consider a group of flexible loads with each load requiring a constant power level for a specified duration before a specified deadline. A load is indifferent of the actual time of delivery as long as the duration and deadline requirements are satisfied. We first address the adequacy problem of a given supply profile which boils down to solving a (0, 1)-matrix feasibility problem. It turns out that the adequacy condition is given explicitly by the nonnegativity of a structure matrix. We also develop a market implementation of the proposed energy service and show the existence of an efficient competitive equilibrium.