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We investigate the problem of fine-grained sketch-based image retrieval (SBIR), where free-hand human sketches are used as queries to perform instance-level retrieval of images. This is an extremely challenging task because (i) visual comparisons not only need to be fine-grained but also executed cross-domain,(ii) free-hand (finger) sketches are highly abstract, making fine-grained matching harder, and most importantly (iii) annotated cross-domain sketch-photo datasets required for training are scarce, challenging many state-of-the-art machine learning techniques. In this paper, for the first time, we address all these challenges, providing a step towards the capabilities that would underpin a commercial sketch-based image retrieval application. We introduce a new database of 1,432 sketch-photo pairs from two categories with 32,000 fine-grained triplet ranking annotations. We then develop a deep triplet-ranking model for instance-level SBIR with a novel data augmentation and staged pre-training strategy to alleviate the issue of insufficient fine-grained training data. Extensive experiments are carried out to contribute a variety of insights into the challenges of data sufficiency and over-fitting avoidance when training deep networks for fine-grained cross-domain ranking tasks.