The fat-tree is one of the most common topologies among the interconnection networks of the systems currently used for high-performance parallel computing. Among other advantages, fat-trees allow the use of simple but very efficient routing schemes. One of them is a deterministic routing algorithm that has been recently proposed, offering a similar (or better) performance than adaptive routing while reducing complexity and guaranteeing in-order packet delivery. However, as other deterministic routing proposals, this deterministic routing algorithm cannot react when high traffic loads or hot-spot traffic scenarios produce severe contention for the use of network resources, leading to the appearance of Head-of-Line (HoL) blocking, which spoils the network performance. In that sense, we describe in this paper two simple, cost-effective strategies for dealing with the HoL-blocking problem that may appear in fat-trees with the aforementioned deterministic routing algorithm. From the results presented in the paper, we conclude that, in the mentioned environment, these proposals considerably reduce HoL-blocking without significantly increasing switch complexity and the required silicon area. Copyright © 2011 John Wiley & Sons, Ltd.