A process for preparing a cable core having a crosslinked insulation layer, said process comprising: (a) providing an initial cable core comprising: (i) a conductor; (ii) a first polymeric semiconductive layer; (iii) an initial insulation layer comprising a crosslinkable polymeric composition which comprises an ethylene-based polymer, an organic peroxide, and a polyallyl crosslinking coagent; (iv) a second polymeric semiconductive layer; and (b) subjecting said initial cable core to a crosslinking process sufficient to crosslink at least a portion of said crosslinkable polymeric composition to thereby produce said cable core having a crosslinked insulation layer, wherein said polyallyl crosslinking coagent and said organic peroxide are present in said crosslinkable polymeric composition in amounts sufficient to provide an allyl-to-active oxygen molar ratio of less than 1.2, based on the allyl content of said polyallyl crosslinking coagent and the active oxygen content of said organic peroxide, wherein when said crosslinked insulation layer is subjected to a degassing process at 70 °C and standard pressure, said crosslinked insulation layer exhibits a reduction in degassing time of at least 50 % to reach a methane content of 200 ppm relative to a reference crosslinked insulation layer having the same composition except that the reference crosslinked insulation layer contains no polyallyl crosslinking coagent and twice the amount of organic peroxide on a weight basis; wherein said organic peroxide is present in said crosslinkable polymeric composition in an amount of less than 1.1 weight percent based on the total weight of said crosslinkable polymeric composition. (a) providing an initial cable core comprising: (i) a conductor; (ii) a first polymeric semiconductive layer; (iii) an initial insulation layer comprising a crosslinkable polymeric composition which comprises an ethylene-based polymer, an organic peroxide, and a polyallyl crosslinking coagent; (iv) a second polymeric semiconductive layer; and (i) a conductor; (ii) a first polymeric semiconductive layer; (iii) an initial insulation layer comprising a crosslinkable polymeric composition which comprises an ethylene-based polymer, an organic peroxide, and a polyallyl crosslinking coagent; (iv) a second polymeric semiconductive layer; and (b) subjecting said initial cable core to a crosslinking process sufficient to crosslink at least a portion of said crosslinkable polymeric composition to thereby produce said cable core having a crosslinked insulation layer, wherein said polyallyl crosslinking coagent and said organic peroxide are present in said crosslinkable polymeric composition in amounts sufficient to provide an allyl-to-active oxygen molar ratio of less than 1.2, based on the allyl content of said polyallyl crosslinking coagent and the active oxygen content of said organic peroxide, wherein when said crosslinked insulation layer is subjected to a degassing process at 70 °C and standard pressure, said crosslinked insulation layer exhibits a reduction in degassing time of at least 50 % to reach a methane content of 200 ppm relative to a reference crosslinked insulation layer having the same composition except that the reference crosslinked insulation layer contains no polyallyl crosslinking coagent and twice the amount of organic peroxide on a weight basis; wherein said organic peroxide is present in said crosslinkable polymeric composition in an amount of less than 1.1 weight percent based on the total weight of said crosslinkable polymeric composition.