For a closed 3-manifold admitting a nonsingular Morse-Smale flow, it is proved that it admits a smooth flow with a nonwandering set disjointly splitting as a union of finitely many hyperbolic closed orbits and a transitive isolated set, without periodic orbits, that is singular-hyperbolic. By the latter property, the system has hyperbolic singularities and exhibits a dominated splitting \(E^s\oplus E^c\) where \(E^s\) (the stable part) is contracting and \(E^c\) (the central part) is volume expanding. The lack of periodic orbits in these examples settles a question raised in this context. As a consequence, any 3-manifold allows for transitive, isolated, singular-hyperbolic sets without periodic orbits.