A stratified body of fluid with compensating horizontal temperature and salinity gradients can undergo an interleaving instability which takes the form of almost horizontal intrusions. As the amplitude of these intrusions grows they can undergo secondary instabilities which eventually leads to the mixing of the fluid in the interior of the intrusions. A previous study of the secondary instabilities focused on two-dimensional disturbances. These corresponded to experimental observations of that time which all seemed to indicate that flows were indeed two-dimensional. Some more recent experiments have shown that the initial secondary instability can make the flow three-dimensional, with the secondary instabilities taking the form of rolls with their axes aligned with the direction of the flow in the intrusions. Here we present a three dimensional stability analysis of steady finite-amplitude intrusions and look at the circumstances which can lead to the three-dimensional instabilities being more likely to be observed.