A study of magnetic avalanches in Perminvar, an Fe-Ni-Co alloy, shows that some avalanches are almost exactly reproducible from one magnetic field cycle to the next, while others show significant variability. Averaging over many cycles produces a fingerprint reflecting the reproducibility of the noise. The fingerprint is not strongly temperature or driving-rate dependent, indicating that the variability is a consequence of dynamical effects. We also find that the slope of the cycle-averaged magnetization, d[M]/dH, is correlated with the cycle-to-cycle variations in magnetization, [(delta M)(2)].