Tsunami warning traditionally has been perceived within the scientific community as an essentially deterministic process. This may be satisfactory in regions where tsunami monitoring is very extensive and the uncertainty in tsunami forecasting is low. However, where there is significant uncertainty, the worthy aspiration to achieve a zero-tolerance policy on tsunami fatalities is set against the reduction in public alert compliance associated with previous false alerts. A risk-informed approach is presented, which outlines a decision process that allows for a decline in alert compliance due to false alerts. This risk-informed approach assesses probabilistically the tsunamigenicity of fault rupture, using data not just from historical catalogues but also the geological record. Prior probabilities could be automatically updated in real time by a Bayesian Belief Network from observations obtained in real time: earthquake depth information; pressure sensor recordings, tide gauge measurements; or visual reports of coastal inundation. A decision to issue a general evacuation warning in a specific region might be made provided the updated posterior probability reached a critical threshold.