The generation of ultrashort pulses hinges on the careful management of dispersion. Traditionally, this has exclusively involved second-order dispersion, while higher-order dispersion was treated as a nuisance to be minimized. Here we show that high-order dispersion can be strategically leveraged to access an uncharted regime of ultrafast laser operation. In particular, we demonstrate a modelocked laser, with an intra-cavity spectral pulse-shaper, that emits pure-quartic soliton pulses, which arise from the interaction of the fourth-order dispersion and the Kerr nonlinearity. Using phaseresolved measurements we demonstrate that the energy of these pulses is proportional to the third power of the inverse pulse duration. This implies a dramatic increase in the energy of ultrashort pulses compared to those emitted by soliton lasers to date. These results not only demonstrate a novel approach to ultrafast lasers, but more fundamentally, they clarify the use of higher-order dispersion for optical pulse control, opening up a plethora of possibilities in nonlinear optics and its applications.