A curable silicone rubber composition, comprising: at least one organopolysiloxane A having at least two alkenyl group bonded to the Si-atom per molecule, or the combination of said at least one organopolysiloxane A with at least one organopolysiloxane resin A', at least one organosiloxane B or organosiloxane resin B' having at least two hydrogen atoms bonded to the same or different Si-atom per molecule, or the mixture of organosiloxane B and organosiloxane resin B' having at least one hydrogen atoms bonded to the same or different Si-atom per molecule, at least one platinum group metal based catalyst C, and at least one tackifier component D, which comprises a) an alkenyl or hydrosilyl group containing isocyanurate compound E of the following formula III: wherein R 1 independently from each other represents methyl, ethyl, propyl, butyl, vinyl, allyl, glycidyl, 1-trimethoxysilyl propyl, tetramethyl cyclotetrasiloxane groups, provided that at least one group R 1 comprises alkenyl or hydrosilyl group, and b) an adhesion-imparting ingredient which is consisting of: - a polysiloxane F having at least two functional groups selected from alkenyl, epoxy, alkoxy and hydrosilyl groups, and - optionally coupling agents G, wherein the amount of coupling agents does not exceed 80% by weight in said adhesion-imparting ingredient. at least one organopolysiloxane A having at least two alkenyl group bonded to the Si-atom per molecule, or the combination of said at least one organopolysiloxane A with at least one organopolysiloxane resin A', at least one organosiloxane B or organosiloxane resin B' having at least two hydrogen atoms bonded to the same or different Si-atom per molecule, or the mixture of organosiloxane B and organosiloxane resin B' having at least one hydrogen atoms bonded to the same or different Si-atom per molecule, at least one platinum group metal based catalyst C, and at least one tackifier component D, which comprises a) an alkenyl or hydrosilyl group containing isocyanurate compound E of the following formula III: wherein R 1 independently from each other represents methyl, ethyl, propyl, butyl, vinyl, allyl, glycidyl, 1-trimethoxysilyl propyl, tetramethyl cyclotetrasiloxane groups, provided that at least one group R 1 comprises alkenyl or hydrosilyl group, and b) an adhesion-imparting ingredient which is consisting of: - a polysiloxane F having at least two functional groups selected from alkenyl, epoxy, alkoxy and hydrosilyl groups, and - optionally coupling agents G, wherein the amount of coupling agents does not exceed 80% by weight in said adhesion-imparting ingredient. a) an alkenyl or hydrosilyl group containing isocyanurate compound E of the following formula III: wherein R 1 independently from each other represents methyl, ethyl, propyl, butyl, vinyl, allyl, glycidyl, 1-trimethoxysilyl propyl, tetramethyl cyclotetrasiloxane groups, provided that at least one group R 1 comprises alkenyl or hydrosilyl group, and b) an adhesion-imparting ingredient which is consisting of: - a polysiloxane F having at least two functional groups selected from alkenyl, epoxy, alkoxy and hydrosilyl groups, and - optionally coupling agents G, wherein the amount of coupling agents does not exceed 80% by weight in said adhesion-imparting ingredient. - a polysiloxane F having at least two functional groups selected from alkenyl, epoxy, alkoxy and hydrosilyl groups, and - optionally coupling agents G, wherein the amount of coupling agents does not exceed 80% by weight in said adhesion-imparting ingredient.