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Sets of E- to NE-trending sinistral and/or reverse faults occur within the San Andreas system, and are associated with palaeomagnetic evidence for clockwise vertical-axis rotations. These structures cut across the trend of active dextral faults, posing questions as to how displacement is transferred across them. Geodetic data show that they lie within an overall dextral shear field, but the data are commonly interpreted to indicate little or no slip, nor any significant rate of rotation. We model these structures as rotating by bookshelf slip in a dextral shear field, and show that a combination of sinistral slip and rotation can produce the observed velocity field. This allows prediction of rates of slip, rotation, fault-parallel extension and fault-normal shortening within the panel. We use this method to calculate the kinematics of the central segment of the Garlock Fault, which cuts across the eastern California shear zone at a high angle. We obtain a sinistral slip rate of 6.1 +/- 1.1 mm yr(-1), comparable to geological evidence, but higher than most previous geodetic estimates, and a rotation rate of 4.0 +/- 0.7 degrees Myr(-1) clockwise. The western Transverse Ranges transect a similar shear zone in coastal and offshore California, but at an angle of only 40 degrees. As a result, the faults, which were sinistral when they were at a higher angle to the shear zone, have been reactivated in a dextral sense at a low rate, and the rate of rotation of the panel has decreased from its long-term rate of similar to 5 degrees to 1.6 degrees +/- 0.2 degrees Myr(-1) clockwise. These results help to resolve some of the apparent discrepancies between geological and geodetic slip-rate estimates, and provide an enhanced understanding of the mechanics of intracontinental transform systems.