While previous research underscores the role of leaders in stimulating employee voice behaviour, comparatively little is known about what affects leaders’ support for such constructive but potentially threatening employee behaviours. We introduce leader member exchange quality (LMX) as a central predictor of leaders’ support for employees’ ideas for constructive change. Apart from a general benefit of high LMX for leaders’ idea support, we propose that high LMX is particularly critical to leaders’ idea support if the idea voiced by an employee constitutes a power threat to the leader. We investigate leaders’ attribution of prosocial and egoistic employee intentions as mediators of these effects. Hypotheses were tested in a quasi‐experimental vignette study (N = 160), in which leaders evaluated a simulated employee idea, and a field study (N = 133), in which leaders evaluated an idea that had been voiced to them at work. Results show an indirect effect of LMX on leaders’ idea support via attributed prosocial intentions but not via attributed egoistic intentions, and a buffering effect of high LMX on the negative effect of power threat on leaders’ idea support. Results differed across studies with regard to the main effect of LMX on idea support.