  The general problem of constructing confidence regions is unsolved in the
sense that there is no algorithm that provides such a region with guaranteed
coverage for an arbitrary parameter $\psi\in\Psi.$ Moreover, even when such a
region exists, it may be absurd in the sense that either the set $\Psi$ or the
null set $\phi$ is reported with positive probability. An approach to the
construction of such regions with guaranteed coverage and which avoids
absurdity is applied here to several problems that have been discussed in the
recent literature and for which some standard approaches produce absurd
regions.
