We demonstrate that the low-frequency noise in our edge junction dc superconducting quantum interference devices, with a basic 1/f flux noise of 2×10−12 Φ20/Hz at 1 Hz, can all be accounted for in terms of junction critical current fluctuations. A novel modulation readout scheme is able to cancel the effect of junction critical current fluctuations and reduce our total noise to 1×10−12 Φ20/Hz at 0.1 Hz, a level that is three times lower than the lowest flux noise ever previously reported at this frequency.