Sawtooth oscillations with two periods and amplitudes per cycle have been observed by the soft-X-ray diodes on the Doublet HI tokamak, most often during beam heating at high current. A theoretical model for such double sawteeth is proposed, in which both disruptions in a cycle are due to magnetic reconnection associated with islands formed about q = 1 surfaces (where q is the safety factor). The second reconnection, which causes the larger disruption, encompasses the magnetic axis as in previous models, whereas the first reconnection does not. Numerical, transport simulations using the new model give results in qualitative agreement with those observed experimentally and imply that the sawtooth-induced energy transport from double sawteeth is essentially the same as that due to single sawteeth of the same cycle length.