This paper illustrates an approach that can refine mechanisms and obtain information about rate constants from dynamical phase diagrams which show the regions of oscillation of a mechanism as a function of the experimental parameters. Possible mechanisms for the experimentally oscillating oxalate-persulfate-silver system are examined. Starting with a proposed mechanism by Ouyang and de Kepper, which they could not make oscillate, we show that some variations of the mechanism are stable for all nonnegative values of the rate constants. Other variations are unstable. For these variations, feedback cycles that lead to instability are compared with a conceptual picture of feedback in the experimental system. One unstable mechanism fits the picture well. Its unimportant reactions are omitted and an analytical solution for the unstable region using 13 adjustable parameters is obtained. The rate constants are adjusted to match this solution to the experimentally measured phase diagram. A good fit can only be obtained if [ O2 ] is too low and k1 is much smaller than the known value. Both discrepancies are resolved if Ag2+ oxidizes water. The analysis predicts the width of the unstable region can increase when more O2 enters the reactor.