Subaerial rock slopes may generate a tsunami by rapidly moving into the water. Large uncertainty in landslide characteristics propagates into large uncertainty in tsunami hazard, making hazard assessment more difficult for land and emergency managers. Once a potentially tsunamigenic landslide is identified, it may not be clear which landslide characteristics contribute most significantly to uncertainty in the tsunami hazard. Our aim is to document the relative worth of different landslide characteristics (e.g., size, material properties) for reducing uncertainty in landslide-tsunami hazard assessments. Isolating the relative importance of specific landslide characteristics may inform prioritization of data collection and improve efficiency in understanding hazard. To accomplish this, we generated a set of 288 landslide-tsunami simulations in which we systematically varied the size and material properties of possible failure extents at the Barry Arm landslide complex in northwestern Prince William Sound, Alaska, USA. We find that for landslides smaller than the receiving waterbody, the landslide volume has the strongest effect on resulting wave characteristics and thus the highest leverage on reducing uncertainty in tsunami hazard. In contrast, for landslides substantially larger than the waterbody, the duration of rapid movement of the landslide has the highest leverage. Based on our results, we propose a classification scheme for subaerial landslides based on the relative size of the landslide and waterbody. Additionally, our results support the generation of a tsunami height transfer function between existing tide gages and a nearby coastal city. These results have direct implications for the practice of operational early warning.