We present a study of p anti-p collisions with a leading
antiproton and a rapidity gap in addition to that associated with the
antiproton. The second gap is either within the region available to the
proton dissociation products, pbar + p --> (pbar + gap) + X + gap + Y, or
adjacent to the outgoing proton pbar + p --> (pbar + gap) + X + (gap + p).
Results are reported for two-gap to one-gap event ratios and compared with
one-gap ratios and with theoretical expectations.