Abstract: A rear carrier or rack for a bicycle has an elongated platform with a pair of side legs attachable to rear frame eyelets. A slide block is supported on the front end portion of the platform and has a pair of spaced, parallel, open sided channels comprising guideways for a pair of slide rods extending beyond the front of the carrier. Lock screws, carried by the rods, extend through open slots in the sides of the slide block and hold the rods at a selected degree of extension beyond the carrier. In one embodiment, a transverse bracket is pivotally connected across downturned front end portions of the slide rods for tilting adjustment about a common horizontal axis. The bracket has a first, central aperture, and a second, offset, elongated aperture. The carrier can be mounted in a plurality of positions to level the platform on bicycles with frame sizes ranging from 19 inches to 27 inches by connecting one or the other of the bracket apertures to the front or rear end of the rear caliper brake mounting bolt.