A commutative integral domain Rof finite Krull dimension rthat is neither quasilocal nor integrally closed has exactly  overrings (including Rand its quotient field K) if and only if Rhas a Prüferian integral closure  with a Y-shaped spectrum such that  is a minimal overring of Rand there is a unique overring of Rthat is incomparable with  Examples of such domains Rare given for each positive r, with a generalization to the semiquasilocal case. Characterizations are also given for the finite-dimensional domains Rwith exactly  or  overrings.

integral domain, prime ideal, overring, integral closure, Krull dimension, Prüfer domain, valuation domain, pseudo-valuation domain, irredundant intersection, minimal ring extension.