Large language model agents are often guided by reusable natural-language skills that provide task-specific instructions. Existing work automatically refines these skills by using LLMs to propose and repeatedly incorporate textual edits from agent feedback. We find that the resulting performance depends substantially on which proposed edits are combined, and adding an edit can even degrade the skill. We therefore introduce SkillCombiner, which generates candidate edits and explicitly searches over their combinations. Across various settings, SkillCombiner matches or exceeds a strong baseline in mean performance while reducing optimizer cost by 75.2% and total optimization-stage cost by 21.5% on average. These results show that edit combination is an important optimization target in agent skill refinement.