The traditional paradigm to update retrieval models requires re-computing the embeddings of the gallery data, a time-consuming and computationally intensive process known as backfilling. To circumvent backfilling, Backward-Compatible Learning (BCL) has been widely explored, which aims to train a new model compatible with the old one. Many previous works focus on effectively aligning the embeddings of the new model with those of the old one to enhance the backward-compatibility. Nevertheless, such strong alignment constraints would compromise the discriminative ability of the new model, particularly when different classes are closely clustered and hard to distinguish in the old feature space. To address this issue, we propose to relax the constraints by introducing perturbations to the old feature prototypes. This allows us to align the new feature space with a pseudo-old feature space defined by these perturbed prototypes, thereby preserving the discriminative ability of the new model in backward-compatible learning. We have developed two approaches for calculating the perturbations: Neighbor-Driven Prototype Perturbation (NDPP) and Optimization-Driven Prototype Perturbation (ODPP). Particularly, they take into account the feature distributions of not only the old but also the new models to obtain proper perturbations along with new model updating. Extensive experiments on the landmark and commodity datasets demonstrate that our approaches perform favorably against state-of-the-art BCL algorithms.