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The performance of x-ray free-electron lasers (XFELs) strongly depends on the longitudinal emittance of the electron beam. We show that by reducing the injector drive laser pulse duration, the electron beam peak current can be increased by a factor of 2 or more, resulting in a significant improvement in longitudinal emittance. Comprehensive simulations and measurements carried out at SwissFEL confirm the expected trade-off of moderately higher transverse emittance. This simple approach can be readily adapted to other XFEL facilities.