This research investigates how applying interaction constraints to digital music instruments (DMIs) affects the way that experienced music performers collaborate and find creative ways to make live improvised music on stage. The constraints are applied in two forms: i) Physically implemented on the instruments themselves, and ii) hidden rules that are defined on a network between the instruments and triggered depending on the musical actions of the performers. Six experienced musicians were recruited for a user study which involved rehearsal and performance. Performers were given deliberately constrained instruments containing a touch sensor, speaker, battery and an embedded computer. Results of the study show that whilst constraints can lead to more structured improvisation, the resultant music may not fit with performers' true intentions. It was also found that when external musical material is introduced to guide the performers into a collective convergence, it is likely to be ignored because it was perceived by performers as being out of context.