Silicone compositions which can be crosslinked to form elastomers and comprise organosilicon compounds which have SiC-bonded radicals having aliphatic carbon-carbon multiple bonds and comprise units of the formula R a R 1 b SiO (4-a-b)/2, where the radicals R can be identical or different and are each an optionally substituted, SiC-bonded, aliphatically saturated hydrocarbon radical, the radicals R 1 can be identical or different and are each an optionally substituted, SiC-bonded, aliphatically unsaturated hydrocarbon radical, a is 0, 1, 2 or 3 and b is 0, 1, 2 or 3, with the proviso that the sum a+b is less than or equal to 3 and at least two radicals R 1 are present per molecule, organopolysiloxanes which have Si-bonded hydrogen atoms and comprise units of the formula R 2 c H d SiO (4-c-d)/2, where the radicals R 2 can be identical or different and each have one of the meanings given above for R, c is 0, 1, 2 or 3 and d is 0, 1 or 2, with the proviso that the sum c+d is less than or equal to 3 and there are on average at least three units of the formula with c=d=1 present per molecule, where the content of Si-bonded hydrogen is greater than or equal to 0.7% by weight, essentially linear organopolysiloxanes having terminally Si-bonded hydrogen atoms and a catalyst which promotes the addition of Si-bonded hydrogen onto aliphatic multiple bonds, with the proviso that the molar ratio of Si-bonded hydrogen originating from component and based on 100 parts by weight of composition to the sum of the Si-bonded hydrogen originating from the components and, in each case based on 100 parts by weight of composition, is in the range from 0.05 to 1. organosilicon compounds which have SiC-bonded radicals having aliphatic carbon-carbon multiple bonds and comprise units of the formula R a R 1 b SiO (4-a-b)/2, where the radicals R can be identical or different and are each an optionally substituted, SiC-bonded, aliphatically saturated hydrocarbon radical, the radicals R 1 can be identical or different and are each an optionally substituted, SiC-bonded, aliphatically unsaturated hydrocarbon radical, a is 0, 1, 2 or 3 and b is 0, 1, 2 or 3, with the proviso that the sum a+b is less than or equal to 3 and at least two radicals R 1 are present per molecule, the radicals R can be identical or different and are each an optionally substituted, SiC-bonded, aliphatically saturated hydrocarbon radical, the radicals R 1 can be identical or different and are each an optionally substituted, SiC-bonded, aliphatically unsaturated hydrocarbon radical, a is 0, 1, 2 or 3 and b is 0, 1, 2 or 3, organopolysiloxanes which have Si-bonded hydrogen atoms and comprise units of the formula R 2 c H d SiO (4-c-d)/2, where the radicals R 2 can be identical or different and each have one of the meanings given above for R, c is 0, 1, 2 or 3 and d is 0, 1 or 2, with the proviso that the sum c+d is less than or equal to 3 and there are on average at least three units of the formula with c=d=1 present per molecule, where the content of Si-bonded hydrogen is greater than or equal to 0.7% by weight, the radicals R 2 can be identical or different and each have one of the meanings given above for R, c is 0, 1, 2 or 3 and d is 0, 1 or 2, essentially linear organopolysiloxanes having terminally Si-bonded hydrogen atoms and a catalyst which promotes the addition of Si-bonded hydrogen onto aliphatic multiple bonds,