We compare the source spectra of the 1994 Java tsunami earthquake (MW = 7.9) and its two largest aftershocks. The source spectra of the aftershocks, from teleseismic P-waves, can be fit remarkably well by a standard ω2 model. However, the mainshock shows a lower moment release at periods of 1--20 sec than its aftershocks, although its total moment is 1000 times larger. We analyze this discrepancy by exploring two mechanisms that, in a simple Haskell rupture model, will decrease one of the corner frequencies of the source spectrum: 1. lowering the rupture velocity and 2. lowering the particle (slip) velocity. Both changes maintain an identical spectral drop-off and static stress drop, and result in the characteristic spectral shape of a slow earthquake. These kinematic models can be related to physical rupture parameters by considering the earthquake energy budget. In both cases the radiated seismic energy is lowered, either due to a higher frictional stress during the break-down phase, increasing the fracture energy (case 1), or by an increase in the sliding stress (case 2). We do not suggest that either of these simplified models is the only possible interpretation, but want to illustrate the danger in directly interpreting slow earthquakes as having a low rupture velocity.