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, p-bar + p --> (p-bar + gap) + X + gap + Y, or adjacent to the
outgoing proton p-bar + p --> (p-bar + gap) + X + (gap + p). Results are
reported for two-gap to one-gap event ratios and compared with one-gap to
no-gap ratios and with theoretical expectations.