A method for fastening a rail of an elevator system to a bearing element fixed in an elevator shaft utilizes a clamp set having a clamp and a spacer. The clamp is arranged on a side part of a rail foot arranged on the bearing element whereby the clamp connects to the bearing element in a fastening zone of the clamp and a contact zone of the clamp is situated on a bearing side on an upper face of the side part. The spacer defines a mounting distance between the contact zone and the bearing side such that the clamp is partly elastically and plastically deformed in the fastening zone when connected. The spacer is then at least partially removed so that a distance between the contact zone and the bearing side is reduced.