TestFul is a novel evolutionary testing approach for object-oriented programs with complex internal states. In our preliminary experiments, it already outperformed some of the well-known search-based testing approaches. In this paper we show how TestFul can be further improved by leveraging three efficiency enhancement techniques: seeding, hybridization, and fitness inheritance. We considered four extensions of TestFul: three using each enhancement separately, and one using all of them at the same time. We used these new versions of TestFul to generate tests for six Java classes taken from the literature, public software libraries, and third party benchmarks. We compared the performance of the original TestFul against these new versions. Our results show that each enhancement technique results in a significant speed-up and, even more interesting, the highest improvement is achieved when all the enhancements are combined together.