A method for communication includes estimating a characteristic of communication traffic to be carried by a fat-tree network. Responsively to the estimated characteristic, a subset of the spine switches in the highest level of the network is selected, according to a predetermined selection order, to be active in carrying the communication traffic. In each of the levels of the spine switches below the highest level, the spine switches to be active are selected based on the selected spine switches in a next-higher level. The network is operated so as to convey the traffic between the leaf switches via the active spine switches, while the spine switches that are not selected remain inactive.