This paper presents the contributions of Charles University teams to the WMT24 General Translation task (English to Czech, German and Russian, and Czech to Ukrainian), and the WMT24 Translation into Low-Resource Languages of Spain task.Our most elaborate submission, CUNI-MH for en2cs, is the result of fine-tuning Mistral 7B v0.1 for translation using a three-stage process: Supervised fine-tuning using QLoRA, Contrastive Preference Optimization, and merging of model checkpoints. We also describe the CUNI-GA, CUNI-Transformer and CUNI-DocTransformer submissions, which are based on our systems from the previous year.Our en2ru system CUNI-DS uses a similar first stage as CUNI-MH (QLoRA for en2cs) and follows with transferring to en2ru.For en2de (CUNI-NL), we experimented with a LLM-based speech translation system, to translate without the speech input.For the Translation into Low-Resource Languages of Spain task, we performed QLoRA fine-tuning of a large LLM on a small amount of synthetic (backtranslated) data.