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Ultrashort pulse generation hinges on the careful management of dispersion. Traditionally, this has exclusively involved second-order dispersion, with higher-order dispersion treated as a nuisance to be minimized. Here, we show that this higher-order dispersion can be strategically leveraged to access an uncharted regime of ultrafast laser operation. In particular, our mode-locked laser—with an intracavity spectral pulse shaper—emits pure-quartic soliton pulses that arise from the interaction of fourth-order dispersion and the Kerr nonlinearity. Phase-resolved measurements demonstrate that their pulse energy scales with the third power of the inverse pulse duration. This implies a strong increase in the energy of short pure-quartic solitons compared with conventional solitons, for which the energy scales as the inverse of the pulse duration. 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, enabling innovations in nonlinear optics and its applications.