Defect prediction models focus on identifying defect-prone code elements, for example to allow practitioners to allocate testing resources on specific subsystems and to provide assistance during code reviews. While the research community has been highly active in proposing metrics and methods to predict defects on long-term periods (i.e., at release time), a recent trend is represented by the so-called short-term defect prediction (i.e., at commit-level). Indeed, this strategy represents an effective alternative in terms of effort required to inspect files likely affected by defects. Nevertheless, the granularity considered by such models might be still too coarse. Indeed, existing commit-level models highlight an entire commit as defective even in cases where only specific files actually contain defects. In this paper, we first investigate to what extent commits are partially defective; then, we propose a novel fine-grained just-in-time defect prediction model to predict the specific files, contained in a commit, that are defective. Finally, we evaluate our model in terms of (i) performance and (ii) the extent to which it decreases the effort required to diagnose a defect. Our study highlights that: (1) defective commits are frequently composed of a mixture of defective and non- defective files, (2) our fine-grained model can accurately predict defective files with an AUC-ROC up to 82% and (3) our model would allow practitioners to save inspection efforts with respect to standard just-in-time techniques.