Root cause analysis (RCA) for incidents in large-scale cloud systems is a complex, knowledge-intensive task that often requires significant manual effort from on-call engineers (OCEs). Improving RCA is vital for accelerating the incident resolution process and reducing service downtime and manual efforts. Recent advancements in Large-Language Models (LLMs) have proven to be effective in solving different stages of the incident management lifecycle including RCA. However, existing LLM-based RCA recommendations typically leverage default finetuning or retrieval augmented generation (RAG) methods with static, manually designed prompts, which lead to sub-optimal recommendations. In this work, we leverage ‘PromptWizard’, a state-of-the-art prompt optimization technique, to automatically identify the best optimized prompt instruction that is combined with semantically similar historical examples for querying underlying LLMs during inference. Moreover, by utilizing more than 180K historical incident data from Microsoft, we developed cost-effective finetuned small language models (SLMs) for RCA recommendation generation and demonstrate the power of prompt optimization on such domain-adapted models. Our extensive experimental results show that ‘PromptWizard’ can improve the accuracy of RCA recommendations by 21% and 13% on 3K test incidents over RAG-based LLMs and finetuned SLMs, respectively. Lastly, our human evaluation with incident owners have demonstrated the efficacy of prompt optimization on RCA recommendation tasks. These findings underscore the advantages of incorporating prompt optimization into AI for Operations (AIOps) systems, delivering substantial gains without increasing computational overhead.