A recent line of work on black-box adversarial attacks has revived the use of transfer from surrogate models by integrating it into query-based search. However, we find that existing approaches of this type underperform their potential, and can be overly complicated besides. Here, we provide a short and simple algorithm which achieves state-of-the-art results through a search which uses the surrogate network's class-score gradients, with no need for other priors or heuristics. The guiding assumption of the algorithm is that the studied networks are in a fundamental sense learning similar functions, and that a transfer attack from one to the other should thus be fairly "easy". This assumption is validated by the extremely low query counts and failure rates achieved: e.g. an untargeted attack on a VGG-16 ImageNet network using a ResNet-152 as the surrogate yields a median query count of 6 at a success rate of 99.9%. Code is available at https://github.com/fiveai/GFCS.