Abstract: There has been significant recent progress in training differentially private (DP) models which achieve accuracy that approaches the best non-private models. These DP models are typically pretrained on large public datasets and then fine-tuned on downstream datasets that are (i) relatively large, and (ii) similar in distribution to the pretraining data. However, in many applications including personalization, it is crucial to perform well in the few-shot setting, as obtaining large amounts of labeled data may be problematic; and on images from a wide variety of domains for use in various specialist settings. To understand under which conditions few-shot DP can be effective, we perform an exhaustive set of experiments that reveals how the accuracy and vulnerability to attack of few-shot DP image classification models are affected as the number of shots per class, privacy level, model architecture, dataset, and subset of learnable parameters in the model vary. We show that to achieve DP accuracy on par with non-private models, the shots per class must be increased as the privacy level increases by as much as 32$\times$ for CIFAR-100 at $\epsilon=1$. We also find that few-shot non-private models are highly susceptible to membership inference attacks. DP provides clear mitigation against the attacks, but a small $\epsilon$ is required to effectively prevent them.