The maximum auroral kilometric radiation (AKR) power flux observed by distant satellites has been increased by more than a factor of 10 from previously reported values. This increase has been achieved by a new data selection criterion and a new analysis of antenna spin modulated signals received by the radio astronomy instrument on ISEE 3. The method relies on selecting AKR events containing signals in the highest-frequency channel (1980, kHz), followed by a careful analysis that effectively increased the instrumental dynamic range by more than 20 dB by making use of the spacecraft antenna gain diagram during a spacecraft rotation. This analysis has allowed the separation of real signals from those created in the receiver by overloading. Many signals having the appearance of AKR harmonic signals were shown to be of spurious origin. During one event, however, real second harmonic AKR signals were detected even though the spacecraft was at a great distance (17 RE) from Earth. During another event, when the spacecraft was at the orbital distance of the Moon and on the morning side of Earth, the power flux of fundamental AKR was greater than 3¿10-13 W m-2 Hz-1 at 360 kHz normalized to a radial distance r of 25 RE assuming hte power falls off as r-2. A comparison of these intense signal levels with the most intense source region values (obtained by ISIS 1 and Viking) suggests that multiple sources were observed by ISEE 3.