This paper presents the novel Droop-e grid-forming inverter control strategy, which establishes an active powerfrequency relationship based on an exponential function of the inverter power dispatch. The advantages of this control strategy include an increased utilization of available headroom, mitigated system frequency dynamics, and a natural limiting behavior, all of which are directly compared to the hitherto standard static droop approach. First, the small signal stability of the Droop-e control is assessed on a 3-bus system and found stable across all possible inverter power dispatches. Then, time-domain simulations show improved frequency dynamics at lower power dispatches, and a limiting behavior at higher dispatches. Finally, a novel secondary control scheme is introduced that achieves power sharing following the primary Droop-e response to load perturbations, which is shown to be effective in time-domain simulations of the 3-and 9-bus systems; comparative simulations with a static 5% droop yields unacceptable frequency deviations, highlighting the superiority of the Droop-e control.