Control for safety and nonblockingness using a deterministic supervisor requires the specification language be controllable and observable (under the setting that marking is also decided by a supervisor). We argue that there exist cases where the above properties do not hold, yet a safe and nonblocking control can be synthesized by allowing the supervisor to be nondeterministic. Use of a nondeterministic supervisor yields a controlled system that is nondeterministic for which a language equivalence only preserve the safety but not the nonblocking property, and so instead we require the stronger equivalence of bisimilarity (which preserves "sequential" behavior such as safety as well as "branching" behavior such as nonblockingness). This motivates us to consider control of deterministic systems for achieving bisimulation equivalence to possibly nondeterministic specifications. We introduce the notions of state-achievability (SA) and state-achievability-bisimilar (SAB) as part of the existence condition, and develop effective algorithms for verify the existence conditions as well as for synthesizing a supervisor when the existence condition holds. We show that the complexity of verifying the existence of a controller is polynomial, whereas that of computing a controller (when one exists) is singly exponential. The proposed approach can be applied to enforce any property that depends on branching and sequential behavior.