  Sobolev mappings exhibiting only pointwise quasiregularity-type bounds have
arisen in various applications, leading to a recently developed theory of
quasiregular values. In this article, we show that by using rescaling, one
obtains a direct bridge between this theory and the classical theory of
quasiregular maps. More precisely, we prove that a non-constant mapping $f
\colon \Omega \to \mathbb{R}^n$ with a $(K, \Sigma)$-quasiregular value at
$f(x_0)$ can be rescaled at $x_0$ to a non-constant $K$-quasiregular mapping.
Our proof of this fact involves establishing a quasiregular values -version of
the linear distortion bound of quasiregular mappings. A quasiregular values
variant of the small $K$ -theorem is obtained as an immediate corollary of our
main result.
