A method for communication includes configuring a multi-level fat-tree network to include at least three levels of switches, including multiple modules arranged externally in a tree topology. Each module contains a respective group of the switches arranged in an internal tree extending over at least two of the levels of the network. A subset of the modules is selected to be active in carrying the communication traffic. The network is operated so as to convey communication traffic among the switches via the active modules, while the modules that are not in the selected subset remain inactive.