  We study the interference between the amplitudes for $gg \rightarrow X
\rightarrow gg$, where $X$ is a new heavy digluon resonance, and the QCD
background $gg \rightarrow gg$, at the Large Hadron Collider. The interference
produces a large low-mass tail and a deficit of events above the resonance
mass, compared to the naive pure resonance peak. For a variety of different
resonance quantum numbers and masses, we evaluate the signal-background
interference contribution at leading order, including showering, hadronization,
and detector effects. The resulting new physics dijet mass distribution may
have a shape that appears, after QCD background fitting and subtraction, to
resemble an enhanced peak, a shelf, a peak/dip, or even a pure dip. We argue
that the true limits on new digluon resonances are likely to differ
significantly from the limits obtained when interference is neglected,
especially if the branching ratio to $gg$ is less than 1.
