Let \(A\) be a noetherian integral domain, \(\overline A\) its integral closure, and let \({\mathcal G}\) be the set of prime ideals \(P\) of \(A\) with height\((P) \leq 1\). The author provides three equivalent conditions for the equality \(\overline A = \bigcap \overline A_P\), \(P \in {\mathcal G}\). For instance, equality holds iff \(\bigcap A_P\), \(P \in {\mathcal G}\), is an integral extension of \(A\) (in particular, rings with a canonical module do have this property); or, equivalently, if height-one primes of \(\overline A\) contract to height-one primes of \(A\).