  For the purpose of cross-fertilising currently separate experimental
approaches, we connect results of LHC analyses attempting to access the
properties of additional $W^\prime$ and $Z^\prime$ bosons from Drell-Yan
processes. Under theoretical assumptions linking the two new gauge bosons, we
take into account that such possible states of nature are wide enough (in
relation to the leptonic mass resolution) for the corresponding signals be
significantly affected by interference effects with the background from the
Standard Model. The shape of the differential cross section may then no longer
be a standard Breit-Wigner distribution, and asymmetry observables would become
useful for characterisation (and, possibly, discovery) purposes. Under such
conditions we concentrate our analysis on specific widely-studied models: the
Sequential Standard Model, a model with an additional $SU(2)_L$ gauge symmetry,
as well as standard and alternative realisations of the Left-Right Symmetric
Model. We show how information gathered in $Z'$ boson searches in terms of
cross section and/or asymmetry distributions can be used to improve $W'$ boson
searches in terms of the LHC sensitivity, and {\it vice versa}.
