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Model compression by way of parameter pruning, quantization, or distillation has recently gained popularity as an approach for reducing the computational requirements of modern deep neural network models for NLP. Inspired by prior works suggesting a connection between simpler, more generalizable models and those that lie within wider loss basins, we hypothesize that optimizing for flat minima should lead to simpler parameterizations and thus more compressible models. We propose to combine sharpness-aware minimization (SAM) with various task-specific model compression methods, including iterative magnitude pruning (IMP), structured pruning with a distillation objective, and post-training dynamic quantization. Empirically, we show that optimizing for flatter minima consistently leads to greater compressibility of parameters compared to vanilla Adam when fine-tuning BERT models, with little to no loss in accuracy on the GLUE text classification and SQuAD question answering benchmarks. Moreover, SAM finds superior winning tickets during IMP that 1) are amenable to vanilla Adam optimization, and 2) transfer more effectively across tasks. 1 Dataset MNLI QQP STS-B QNLI MRPC RTE SST-2 CoLA SQuAD Sparsity 70% 90% 50% 70% 50% 60% 60% 50% 40% Metric Match/Mismatch acc. Acc.