Identifying which fingers are touching a multi-touch surface provides a very large input space. We describe FingerCuts, an interaction technique inspired by desktop keyboard shortcuts to exploit this potential. FingerCuts enables integrated command selection and parameter manipulation, it uses feed-forward and feedback to increase discoverability, it is backward compatible with current touch input techniques, and it is adaptable for different touch device form factors. We implemented three variations of FingerCuts, each tailored to a different device form factor: tabletop, tablet, and smartphone. Qualitative and quantitative studies conducted on the tabletop suggests that with some practice, FingerCuts is expressive, easy-to-use, and increases a sense of continuous interaction flow and that interaction with FingerCuts is as fast, or faster than using a graphical user interface. A theoretical analysis of FingerCuts using the Fingerstroke-Level Model (FLM) matches our quantitative study results, justifying our use of FLM to analyse and validate the performance for the other device form factors.