Neural network models often generalize poorly to mismatched domains or\ndistributions. In NLP, this issue arises in particular when models are expected\nto generalize compositionally, that is, to novel combinations of familiar words\nand constructions. We investigate learning representations that facilitate\ntransfer learning from one compositional task to another: the representation\nand the task-specific layers of the models are strategically trained\ndifferently on a pre-finetuning task such that they generalize well on\nmismatched splits that require compositionality. We apply this method to\nsemantic parsing, using three very different datasets, COGS, GeoQuery and SCAN,\nused alternately as the pre-finetuning and target task. Our method\nsignificantly improves compositional generalization over baselines on the test\nset of the target task, which is held out during fine-tuning. Ablation studies\ncharacterize the utility of the major steps in the proposed algorithm and\nsupport our hypothesis.\n