The purpose of instruction tuning is enabling zero-shot performance, but instruction tuning has also been shown to improve chain-of-thought reasoning and value alignment (Si et al., 2023). Here we consider the impact on $\textit{consistency}$, i.e., the sensitivity of language models to small perturbations in the input. We compare 10 instruction-tuned LLaMA models to the original LLaMA-7b model and show that almost across-the-board they become more consistent, both in terms of their representations and their predictions in zero-shot and downstream tasks. We explain these improvements through mechanistic analyses of factual recall.