The averaging of Aharonov-Bohm oscillations caused by incomplete phase coherence has been studied in two Sb rings. In these devices, the phase-coherence length L can be determined independently from an analysis of the weak localization contribution to the magnetoconductance (GC) or from the amplitude of the conductance fluctuations. We find that the Aharonov-Bohm oscillations decrease as exp(-LL) where L is the sample length. The values of L inferred from GC qualitatively predict the temperature dependence of the conductance fluctuations. © 1987 The American Physical Society.