  The paper aims at the qualitative criterion of higher-spin locality.
Perturbative analysis of the Vasiliev equations gives rise to the so-called
$z$-dominated non-localities which nevertheless disappear from interaction
vertices leaving the final result spin-local in all known cases. This has led
one to the $z$ -- dominance conjecture that suggests universality of the
observed cancellations. Here we specify conditions which include observation of
the higher-spin shift symmetry and prove validity of this recently proposed
conjecture. We also define a class of spin-local and shift-symmetric field
redefinitions which is argued to be the admissible one with respect to
spin-locality.
