Slack-compensating pulleys, transmission systems including slack-compensating pulleys, and methods of operating these. In general, slack-compensating pulleys include a pulley body onto which a cable can wind, and one or more (e.g., two) slack take-up surfaces that rotate with the pulley body that are configured to remove slack form an outgoing length of cable by increasing the cable path length and wrap angle. In particular, described herein are minimal access tools having slack-compensating transmissions.