  In this paper we present the partial wave unitarity bound in the parameter
space of dimension-5 and dimension-6 effective operators that arise in a
compositeness scenario. These are routinely used in experimental searches at
the LHC to constraint contact and gauge interactions between ordinary Standard
Model fermions and excited (composite) states of mass $M$. After deducing the
unitarity bound for the production process of a composite neutrino, we
implement such bound and compare it with the recent experimental exclusion
curves for Run 2, the High-Luminosity and High-Energy configurations of the
LHC. Our results also applies to the searches where a generic single excited
state is produced via contact interactions. We find that the unitarity bound,
so far overlooked, is quite complelling and significant portions of the
parameter space ($M,\Lambda$) become excluded in addition to the standard
request $M \le \Lambda$.
