  Besicovitch showed that if a set is null for the Hausdorff measure associated
to a given dimension function, then it is still null for the Hausdorff measure
corresponding to a smaller dimension function. We prove that this is not true
for packing measures. Moreover, we consider the corresponding questions for
sets of non-$\sigma$-finite packing measure, and for pre-packing measure
instead of packing measure.
