It is well-known that a deep neural network has a strong fitting capability and can easily achieve a low training error even with randomly assigned class labels. When the number of training samples is small, or the class labels are noisy, networks tend to memorize patterns specific to individual instances to minimize the training error. This leads to the issue of overfitting and poor generalisation performance. This paper explores a remedy by suppressing the network's tendency to rely on instance-specific patterns for empirical error minimisation. The proposed method is based on an adversarial training framework. It suppresses features that can be utilized to identify individual instances among samples within each class. This leads to classifiers only using features that are both discriminative across classes and common within each class. We call our method Adversarial Suppression of Identity Features (ASIF), and demonstrate the usefulness of this technique in boosting generalisation accuracy when faced with small datasets or noisy labels. Our source code is available.