An evolutionary system that supports the interaction of neutral and adaptive mutations is investigated. Experimental results on a Boolean function and needle-in-haystack problems show that this system enables evolutionary search to find better solutions faster. Through a novel analysis based on the ratio of neutral to adaptive mutations, we identify this interaction as an engine that automatically adjusts the relative amounts of exploration and exploitation to achieve effective search (i.e., it is self-adaptive). Moreover, a hypothesis to describe the search process in this system is proposed and investigated. Our findings lead us to counter the arguments of those who dismiss the usefulness of neutrality. We argue that the benefits of neutrality are intimately related to its implementation, so that one must be cautious about making general claims about its merits or demerits.