A carriage for use in a reformer exercise apparatus is disclosed that has a pair of upwardly extending folding shoulder stops mounted thereto at one end and a headrest between the shoulder stops that extends outward from the carriage toward the head end of the frame. A pair of roller wheels at the head end and a pair at the foot end of the carriage support the platform. A single common axle supports the head end pair of rollers from the carriage, forms a pivot support for the folding shoulder stops, and forms part of an adjustable position support assembly for the headrest. The shoulder stops are preferably attached to a tubular sleeve that rotates on the common axle.