The fat-tree is one of the topologies most widely used to build high-performance parallel computers. However, they are expensive and difficult to build. In this paper we propose two alternative tree-like topologies that are cheaper in terms of cost and complexity, because they are “thinner” than fat-trees: less switches, and less links. We test the performance of these narrowed trees, and compare it with that of the full-fledged fat-tree using a collection of synthetic patterns that emulate the behavior of well-known applications, including causal relationships among messages. Moreover, we do a performance/cost analysis of these networks. Our main conclusion is that, for the set of studied applications, performance of narrowed topologies is as high as that of fat-trees, with much less cost. Rearranging switch ports to use them as downward ports instead of upward ports do reduce bisection bandwidth, but also increases locality, which can be efficiently exploited by applications.