An instrument sterile drape includes a plastic sheet and a pouch sealed to a first opening in the plastic sheet. The pouch is shaped to fit around a carriage that includes actuators. An instrument sterile adapter (ISA) is coupled to a second opening in the pouch. The ISA includes a bottom plate and a top plate located on opposite sides of the pouch and joined together. A stiffener may be coupled to the pouch around the second opening to provide a relatively inelastic area that corresponds to a portion of the pouch that is retained between the bottom plate and the top plate. Portions of the bottom plate may project through the top plate to provide a datum plane to receive a surgical instrument. The ISA may contain loose pins that depress sensing pins in the carriage when a surgical instrument is mounted.