The paper presents sufficient conditions for modular (supervisory) control synthesis to equal global control synthesis. In modular control synthesis a supervisory control is synthesized for each module separately and the supervisory control consists of the parallel composition of the modular supervisory controls. The general case of the specification that is indecomposable and not necessarily contained in the plant language, which is often the case in practice, is considered. The usual assumption that all shared events are controllable is relaxed by introducing two new structural conditions relying on the global mutual controllability condition. The novel concept used as a sufficient structural condition is strong global mutual controllability. The main result uses a weaker condition called global mutual controllability together with local consistency of the specification. An example illustrates the approach.