X-ray free-electron lasers (FELs) are powerful tools for probing matter properties down to sub-nanometer scales with femtosecond time resolution, allowing a growing number of physical, chemical, biological and medical investigations to be carried out. FELs operating in seeding mode intrinsically present enhanced temporal coherence properties with respect to those relying on the self-amplified spontaneous emission (SASE) process. They are however limited, for the moment, to extreme ultraviolet (XUV) wavelengths, or in some cases to soft X-rays, and durations of tens of femtoseconds. We studied how these limits can be overcome by means of X-ray chirped pulse amplification, inspired by infrared lasers. As a matter of fact, the use of a seed enables a fine control of the chirp and a spectro-temporal shaping of the FEL emission. Moreover, ultrashort wavelengths can be envisaged through schemes of high-gain harmonic generation and echo-enabled harmonic generation. We will present FEL simulations coupled with the study of a compressor in conical diffraction geometry.