  We address pairs $(X, Y)$ of metric spaces with the following property: for
every mapping $f: X \to Y$ the existence of points $x, y \in X$ with
$d(f(x),f(y)) > d(x,y)$ implies the existence of $\widetilde{x},
\widetilde{y}\in X$ for which $d(f(\widetilde{x}),f(\widetilde{y})) <
d(\widetilde{x},\widetilde{y})$. We give sufficient conditions for this
property and for its uniform version in terms of finite $\varepsilon$-nets and
finite $\varepsilon$-separated subsets.
