Prior work has shown that it is possible to expand pretrained Masked Language Models (MLMs) to new languages by learning a new set of embeddings, while keeping the transformer body frozen. Despite learning a small subset of parameters, this approach is not compute-efficient, as training the new embeddings requires a full forward and backward pass over the entire model. In this work, we propose mini-model adaptation, a compute-efficient alternative that builds a shallow mini-model from a fraction of a large model’s parameters. New language-specific embeddings can then be efficiently trained over the mini-model, and plugged into the aligned large model for rapid cross-lingual transfer. We explore two approaches to learn mini-models: MiniJoint, which jointly pretrains the primary model and the mini-model using a single transformer with a secondary MLM head at a middle layer; and MiniPost, where we start from a regular pretrained model and build a mini-model by extracting and freezing a few layers and learning a small number of parameters on top. Experiments on XNLI, MLQA and PAWS-X show that mini-model adaptation matches the performance of the standard approach using up to 2.4x less compute.