In the design of filters for which it is required that there should be little or no overshoot of the transient response for a step input, it is common practice to adjust parameters so that the binomial filters are realized. This results in relatively slow rise times, but ensures zero overshoot. It is shown in this article that very much faster rise times can be obtained by pole-zero configurations which ensure a non-negative impulse response. The concept differs from traditional methods and also shows that intuitive notions of the response for given pole-zero distributions can be misleading.