The Co2+ ions of the Co1+xCr2-xSe4 phase (Co1.24Cr1.76Se4 composition with x = 0.24, C2/m space group, Cr3S4-type structure) undergo a high- to low-spin-state transition around 230 K, as concluded from the temperature-dependent single-crystal synchrotron radiation diffraction experiments and the previously reported physical property studies. The change of the spin state is not instantaneous and goes through a wide spin-crossover (SCO) region of 75 K. A similar Co2+ high- to low-spin-state transition is suggested at a pressure of 14.5 GPa, as is evident from the pressure-dependent single-crystal synchrotron radiation diffraction experiments. The corresponding SCO region is equal to 5 GPa, and the structural behavior is different from the one observed during the temperature-dependent transition. Coupling between the spin-conversion process in Co1+xCr2-xSe4 and the concomitant changes in the physical properties opens a way for a controlled tuning of the observed physical response through compositional and structural modifications.