In this paper we show that the performance workload of button-input interfaces do not monotonically increase with the number of buttons, but there is an optimal number of buttons in the sense that the performance workload is minimized. As the number of buttons increases, it becomes more difficult to search for the target button, and, as such, the user's cognitive workload is increased. As the number of buttons decreases, the user's cognitive workload decreases but his operational workload increases, i.e., the amount of operations becomes larger because one button has to be used for plural functions. The optimal number of buttons emerges by combining the cognitive and operational workloads. The experiments used to measure performance were such that we were able to describe a multiple regression equation using two observable variables related to the cognitive and operational workloads. As a result, our equation explained the data well and the optimal number of buttons was found to be about 8, similar to the number adopted by commercial cell phone manufacturers. It was clarified that an interface with a number of buttons close to the number of letters in the alphabet was not necessarily easy to use.