A short mathematical essay by Ralph Griswold on twill counters, the notation that describes which shafts are raised and not raised in a twill. It explains stacked and linear (slash) notation, how counters relate to twill tie-ups through rotation, and how to choose a standard form. It then presents a method for enumerating counters by treating them as compositions with an even number of terms, encoded as bit patterns, and distinguishes proper from inherited counters. A table gives counts of twill counters for 2 to 20 shafts.