Some application domains, including monitoring of active systems in artificial intelligence and model-based mutation testing in software engineering, require determinization of finite automata to be performed incrementally. To this end, an algorithm called Incremental Subset Construction (ISC) was proposed a few years ago. However, this algorithm was recently discovered to be incorrect is some instance problems. The incorrect behavior of ISC originates when the redirection of a transition causes a portion of the automaton to be disconnected from the initial state. This misbehavior is disturbing in two ways: portions of the resulting automaton are disconnected and, as such, useless; moreover, a considerable amount of computation is possibly wasted for processing these disconnected parts. To make ISC sound, a metrics-based technique is proposed in this paper, where the distance between states is exploited in order to guarantee the connection of the automaton, thereby allowing ISC to achieve soundness. Experimental results show that, besides being effective, the proposed technique is efficient too.