Low-rank adaptation (LoRA) is a natural method for finetuning in communication-constrained machine learning settings such as cross-device federated learning. Prior work that has studied LoRA in the context of federated learning has focused on improving LoRA's robustness to heterogeneity and privacy. In this work, we instead consider techniques for further improving communication-efficiency in federated LoRA. Unfortunately, we show that centralized ML methods that improve the efficiency of LoRA through unstructured pruning do not transfer well to federated settings. We instead study a simple approach, \textbf{FLASC}, that applies sparsity to LoRA during communication while allowing clients to locally fine-tune the entire LoRA module. Across four common federated learning tasks, we demonstrate that this method matches the performance of dense LoRA with up to $10\times$ less communication. Additionally, despite being designed primarily to target communication, we find that this approach has benefits in terms of heterogeneity and privacy relative to existing approaches tailored to these specific concerns. Overall, our work highlights the importance of considering system-specific constraints when developing communication-efficient finetuning approaches, and serves as a simple and competitive baseline for future work in federated finetuning.