Process for preparing a crosslinked cable, comprising the steps consisting of: - applying on a conductor at least one layer comprising a polymer composition, and one or more organic peroxides, then - crosslinking said layer to obtain a crosslinked cable, then - cooling the obtained crosslinked cable under pressurized conditions, and then - reducing or removing the content of volatile decomposition products(s) generated during crosslinking, at ambient or at elevated temperature, wherein said process comprises one or both of the following features: - said reduction or removal step is carried out in a more than 50% shorter period of time than the time period required for a reference cable that is a crosslinked and cooled cable having the same structure and layer material in each of said one or more layers, and prepared using the same process steps and conditions thereof, as well as the same degree of crosslinking, as said claimed crosslinked and cooled cable, but using a dicumyl peroxide as organic peroxide, in order for said reference cable to obtain the same content of said volatile decomposition product(s) as said claimed cable by using the same reduction or removal conditions as said claimed cable, or - said reduction or removal step is carried out at a lower temperature than the temperature required for a reference cable that is a crosslinked and cooled cable having the same structure and layer material in each of said one or more layers, and prepared using the same process steps and conditions thereof, as well as the same degree of crosslinking, as said claimed crosslinked and cooled cable, but using a dicumyl peroxide as organic peroxide, in order for said reference cable to obtain the same content of said volatile decomposition product(s) as said claimed cable, and wherein said organic peroxide is of formula: where: - n is an integer equal to 1, 2, 3 or 4, - R1, R1' are each independently an oxygen atom, linear or branched, saturated or partially unsaturated C1-C5 hydrocarbyl chain, and preferably a substituted linear C1-C5 alkyl chain, - R2, R2', R3, R3' are each independently a linear or branched, saturated or partially unsaturated C1-C5 hydrocarbyl group, and preferably an unsubstituted linear C1-C5 alkyl group, and - R4, R4' are each independently H, linear or branched, saturated or partially unsaturated C1-C5 hydrocarbyl group, and preferably an unsubstituted linear C1-C5 alkyl group. - applying on a conductor at least one layer comprising a polymer composition, and one or more organic peroxides, then - crosslinking said layer to obtain a crosslinked cable, then - cooling the obtained crosslinked cable under pressurized conditions, and then - reducing or removing the content of volatile decomposition products(s) generated during crosslinking, at ambient or at elevated temperature, wherein - said reduction or removal step is carried out in a more than 50% shorter period of time than the time period required for a reference cable that is a crosslinked and cooled cable having the same structure and layer material in each of said one or more layers, and prepared using the same process steps and conditions thereof, as well as the same degree of crosslinking, as said claimed crosslinked and cooled cable, but using a dicumyl peroxide as organic peroxide, in order for said reference cable to obtain the same content of said volatile decomposition product(s) as said claimed cable by using the same reduction or removal conditions as said claimed cable, or - said reduction or removal step is carried out at a lower temperature than the temperature required for a reference cable that is a crosslinked and cooled cable having the same structure and layer material in each of said one or more layers, and prepared using the same process steps and conditions thereof, as well as the same degree of crosslinking, as said claimed crosslinked and cooled cable, but using a dicumyl peroxide as organic peroxide, in order for said reference cable to obtain the same content of said volatile decomposition product(s) as said claimed cable, and - n is an integer equal to 1, 2, 3 or 4, - R1, R1' are each independently an oxygen atom, linear or branched, saturated or partially unsaturated C1-C5 hydrocarbyl chain, and preferably a substituted linear C1-C5 alkyl chain, - R2, R2', R3, R3' are each independently a linear or branched, saturated or partially unsaturated C1-C5 hydrocarbyl group, and preferably an unsubstituted linear C1-C5 alkyl group, and - R4, R4' are each independently H, linear or branched, saturated or partially unsaturated C1-C5 hydrocarbyl group, and preferably an unsubstituted linear C1-C5 alkyl group.