A curable silicone rubber composition, comprising: (A) 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', (B) 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, (C) at least one platinum group metal based catalyst C, and (D) 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) 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', (B) 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, (C) at least one platinum group metal based catalyst C, and (D) 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. <EOS>