  In the Higgs search at the LHC, a light Higgs boson (115 GeV <~ M_H <~ 130
GeV) is not excluded by experimental data. In this mass range, the width of the
Standard Model Higgs boson is more than four orders of magnitude smaller than
its mass. The zero-width approximation is hence expected to be an excellent
approximation. We show that this is not always the case. The inclusion of
off-shell contributions is essential to obtain an accurate Higgs signal
normalisation at the 1% precision level. For gg (-> H) -> VV, V= W,Z, O(10%)
corrections occur due to an enhanced Higgs signal in the region M_VV > 2 M_V,
where also sizable Higgs-continuum interference occurs. We discuss how
experimental selection cuts can be used to exclude this region in search
channels where the Higgs invariant mass cannot be reconstructed. We note that
the H -> VV decay modes in weak boson fusion are similarly affected.
