Self-adhesive crosslinkable silicone compositions may be transparent and prepared without conventional adhesion promoters, and contain (1) an organopolysiloxane having a minimum of two aliphatically unsaturated carbon-carbon bond-containing groups, (2) a pendant Si—H functional organopolysiloxane having at least 3 Si—H groups and a minimum of 0.7 weight percent of Si-bonded hydrogen, and (3) a linear organopolysiloxane bearing terminal Si—H groups, wherein the mol ratio of silicon-bonded hydrogen in (2) to that in [(2) and (3)] is from 0.05 to 1.