Re-evaluation of magnitude-geographical criterion of tsunami prediction is one of the main directions of improvement of the tsunami warning service acting on the coast of the Russian Far East. The main directions of this work are a careful analysis of the tsunami warnings issued by the service during the period of its operation (since 1958), determining of reasons for false alarms and missed warnings, delineation of tsunamigenic areas threatening the Far East coast of Russia, optimal selection of magnitude thresholds for each tsunamigenic zone, evaluation of the expected ratio between real/missed/false warnings, determination of the degree of influence of other source parameters (focus depth, source mechanism), and evaluation of probability of occurrence for nonseismic tsunamis. The present paper considers the results of operations for prediction of tsunamis from submarine earthquakes that occurred in the Kuril-Kamchatka zone, Sea of Japan, and Sea of Okhotsk during the last 52 years.