Abstract: In this paper, we look at cross-domain few-shot classification which presents the challenging task of learning new classes in previously unseen domains with few labelled examples. Existing methods, though somewhat effective, encounter several limitations, which we alleviate through two significant improvements. First, we introduce a lightweight parameter-efficient adaptation strategy to address overfitting associated with fine-tuning a large number of parameters on small datasets. This strategy employs a linear transformation of pre-trained features, significantly reducing the trainable parameter count. Second, we replace the traditional nearest centroid classifier with a discriminative sample-aware loss function, enhancing the model's sensitivity to the inter- and intra-class variances within the training set for improved clustering in feature space. Empirical evaluations on the Meta-Dataset benchmark showcase that our approach not only improves accuracy up to 7.7\% and 5.3\% on previously seen and unseen datasets, respectively, but also achieves the above performance while being at least $\sim3\times$ more parameter-efficient than existing methods, establishing a new state-of-the-art in cross-domain few-shot learning. Our code is available at https://github.com/rashindrie/DIPA.