An analysis has been made of the three-dimensional trajectories of two components in the parsec-scale jet of BL Lac, constructed using centimetre-wavelength VLBI data at multiple epochs. The 3-D trajectory of each of these components has first been reconstructed assuming that they move with constant speeds. The only plausible trajectories consistent with the observed paths make small angles to the line of sight (less than 15degrees) everywhere along their paths. The flux density variations predicted by variations in Doppler beaming do not agree with the component light curves. We suggest models involving expansion or deceleration in addition to changes in direction to account for the observed flux density changes. (C) 2003 Published by Elsevier B.V.