Understanding how nervous systems generate behavior requires understanding how muscles transform neural input into movement. The stick insect extensor tibiae muscle is an excellent system in which to investigate this issue because extensor motor neuron activity is highly variable during single leg walking and extensor muscles driven with this activity produce highly variable movements (Hooper et al. 2006b). We showed earlier that spike number, not frequency, codes for extensor amplitude during contraction rises, which implies the muscle acts as a slow filter on the time scale of burst interspike intervals (5-10 msec) (Hooper et al. 2006a). We examine here muscle response to spiking variation over entire bursts, a time scale of hundreds of msec, and directly measure muscle time constants. Muscle time constants differ during contraction and relaxation, and contraction time constants, although variable, are always extremely slow (200-700 msec). Models using these data show that extremely slow temporal filtering alone can explain much of the observed transform properties. This work also revealed an unexpected (to us) ability of slow filtering to transform steadily declining inputs into constant amplitude outputs. Examination of the effects of time constant variability on model output showed that variation within a standard deviation of the mean primarily altered output amplitude, but variation across the entire range also altered contraction shape. These substantial changes suggest that understanding the basis of this variation is central to predicting extensor activity, and that the animal could theoretically vary muscle time constant to match extensor response to changing behavioral need.