[eng] This paper proposes three techniques to reduce the computational cost, both in terms of memory and CPU usage, of visual underwater trajectory-based SLAM. On the one hand, geometric constraints involving the camera Field of View (FOV) are used to decide when a new node has to be added to the trajectory estimate. On the other hand, the camera FOV geometry is also used to preselect the candidate images that have to be registered. Finally, the trajectory-based structure is exploited to foresee loop closures and concentrate the computational efforts to these situations, reducing the CPU work when possible. As a result of these three techniques, the resolution of the estimated trajectory is adjusted dynamically and the image registration process, which is usually the most expensive, is only executed with images that are likely to provide useful information.