Search-based software testing (SBST) has been shown to be an effective technique to generate test cases automatically. Its effectiveness strongly depends on the guidance of the fitness function. Unfortunately, a common issue in SBST is the so called flag problem, where the fitness landscape presents a plateau that provides no guidance. In this paper, we provide a series of novel testability transformations aimed at providing guidance in the context of commonly used API calls. An example is when strings need to be converted into valid date/time objects. We implemented our novel techniques as an extension to EVOMASTER, a SBST tool that generates system level test cases. Experiments on six open-source REST web services, and an industrial one, show that our novel techniques improve performance significantly.