In the context of Haag-Kastler nets of local observables, the paper deals with the questions how to assign a smallest localization region to a single, nontrivial, observable \(A\). It is natural to consider to this end the intersection of all regions \(\overline{\mathcal{O}}\) such that \(A\) is contained in \(\mathfrak{A}(\mathcal{O})''\) (or \(\mathfrak{A}(\mathcal{O}')'\)). To show that this makes sense, i.e., leads to a nonempty region for a nontrivial observable, the author employs an empty-intersection theorem which is a generalization of a result due to Landau. The result is valid in \(2+1\) or more spacetime dimensions. Contrary to naïve intuition, it does not follow from locality of the net \(\mathfrak{A}\) that such a prescription of localization regions is again local, i.e., that observables with mutually spacelike smallest localization regions commute in the quasilocal algebra. For this to hold, the author exhibits (under the additional assumption of wedge duality) a necessary and suffucient condition in the form of a nonempty-intersection theorem. It is further shown that the common property of wedge additivity implies this condition. Applications of these results to the Unruh-effect are indicated.