Waterbomb-style tessellations have been explored in the past by artists such as Ronald D. Resch, Benjamin Parker and Mitya Miller. Generalised waterbomb tessellations are still underexplored in origami design. We have explored various sets of criteria for generalising waterbomb tessellations in order to enumerate valid patterns. We only consider triangular waterbomb tessellations; other polygons will be explored in future papers. In our search, we have uncovered some new waterbomb tessellations, which could offer new uses in representational and geometric origami design. We conclude by discussing foldability properties and possible generalisations.