Patients with motor control difficulties often "type" on a computer using a switch keyboard to guide a scanning cursor to text elements. We show how to optimize some parts of the design of switch keyboards by casting the design problem as mixed integer programming. A new algorithm to find an optimized design solution is approximately 3600 times faster than a previous algorithm, which was also susceptible to finding a non-optimal solution. The optimization requires a model of the probability of an entry error, and we show how to build such a model from experimental data. Example optimized keyboards are demonstrated.