The costs of designing, testing and validating a new engine concept are very high. Therefore, the industry is highly motivated to take an existing engine and create a family of derivative engines covering a range of applications, while implementing incremental advances in technology. The heart of an engine is the core, so a frequent approach is to retain the core and design a series of LP/IP spools around it. In this chapter, we take a baseline engine from a small business jet and study how to both increase the thrust capability and improve SFC, while limiting major changes to the LP system. In the worked example, we first define the design variables and select a figure of merit for the derivative engine. We then identify any design constraints, which may come from a range of items such as available technology or installation requirements, environmental regulations, or simply cost of manufacture. The results of the optimization study using GasTurb are evaluated in a series of design space graphs, which identify where design limits are reached.