Tunable lenses are widely applied in imaging systems, as they provide inertia-free axial scanning. Their proper placement in the imaging system is critical to maximize tuning range and to limit broadening of the focal spot size. We introduce a purely analytic description of optical systems employing tunable lenses as a toolset to find application-specific optimal trade-offs between these opposing goals. The proposed method is applied to selected configurations of axial scanning systems to derive analytic expressions for their effective focal length and spot size. On this basis, we provide practical guidelines for the design of axial scanning systems.