  Collider searches for new vector-like particles such as Z' have mostly been
pursued by looking for a peak in the invariant mass spectrum of the decay
products. However off-shell Z' exchange may leave an imprint on other kinematic
distributions, leading thus to non-resonant searches. The aim of this paper is
to assess, in the context of the LHC, the interplay between resonant
(s-channel) and non-resonant (t-channel) searches for a generic leptophobic Z'
model. We show in particular that while non-resonant searches are less
sensitive to small couplings, they tend to be more adapted at high masses and
large couplings. We discuss our findings both at the level of the current
limits and the expectations at higher luminosities.
