An improved technique for determining the thickness of a member, especially pipe such as fluid-filled casing in an earth borehole, includes the following steps: directing a pulse of ultra-sonic energy toward the inner surface of the pipe and receiving/storing, as a function of time, signals representative of ultra-sonic energy reflected from the inner surface of the pipe; determining, from the stored signals, the arrival or the initial echo from the inner surface; determining from the stored signals, the arrival and the amplitude of a first candidate initial echo from the outer surface of the pipe; performing a reverse search on the stored signals to determine, from stored signals at times earlier than the arrival time of the first candidate the arrival and the amplitude of a second candidate initial echo from the outer surface; comparing amplitudes of the first and second candidates and selecting, based on the comparison, one of the first and second candidates as the actual outer surface echo; and determining the thickness of the pipe from the arrival time of the actual outer surface echo and the arrival time of the inner surface echo. Using this technique, the earlier arriving candidate can be properly identified as the actual outer surface echo, even when the later arriving candidate has a greater amplitude.