The well-established methodology for slider-crank function generation states that 5 precision points can be achieved with no structural error. The resulting designs, however, do not necessarily satisfy all of the kinematic requirements for designing the slider-crank linkages used to drive the ram of a mechanical press. First, solutions to the 5 precision point synthesis problem may not have the precision points on one circuit. Additionally, there is no guarantee of a fully rotatable input crank. In this paper we present 4.5 precision point synthesis, a modification to the 5 precision point methodology for designing slider-cranks with fully rotatable input links and all precision points on the same circuit. The 4.5 precision point function generation methodology is illustrated with an example.