Can we improve machine translation (MT) with LLMs by rewriting their inputs automatically? Users commonly rely on the intuition that well-written text is easier to translate when using off-the-shelf MT systems. LLMs can rewrite text in many ways but in the context of MT, these capabilities have been primarily exploited to rewrite outputs via post-editing. We present an empirical study of 21 input rewriting methods with 3 open-weight LLMs for translating from English into 6 target languages. We show that text simplification is the most effective MT-agnostic rewrite strategy and that it can be improved further when using quality estimation to assess translatability. Human evaluation further confirms that simplified rewrites and their MT outputs both largely preserve the original meaning of the source and MT. These results suggest LLM-assisted input rewriting as a promising direction for improving translations.