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We have produced hard x-ray free-electron laser (FEL) pulses, which are chirped both in photon energy and in spatial position. The experiments have been carried out at the hard x-ray beamline Aramis at SwissFEL, located at the Paul Scherrer Institute in Switzerland. The FEL beamline was operated without any external focusing and with a tilted, energy-chirped electron bunch, whose properties are then transferred to the photon beam. The resulting FEL pulses were used for a single-shot absorption x-ray spectroscopy experiment at the Alvra endstation. But, as will be outlined, applications of this type of tailored FEL pulse go beyond such experiments, allowing for x-ray pulse compression and control of the transverse coherence within the pulse.