  A mapping $f:X\to Y$ between metric spaces is called \emph{little Lipschitz}
if the quantity $$
  \operatorname{lip}(f(x)=\liminf_{r\to0}\frac{\operatorname{diam}
f(B(x,r))}{r} $$ is finite for every $x\in X$.
  We prove that if a compact (or, more generally, analytic) metric space has
packing dimension greater than $n$, then $X$ can be mapped onto an
$n$-dimensional cube by a little Lipschitz function.
  The result requires two facts that are interesing in their own right. First,
an analytic metric space $X$ contains, for any $\varepsilon>0$, a compact
subset $S$ that embeds into an ultrametric space by a Lipschitz map, and
$\dim_P S\geq\dim_P X-\varepsilon$. Second, a little Lipschitz function on a
closed subset admits a little Lipschitz extension.
