Radiology report summarization (RRS) is critical for clinical workflows, requiring concise Impressions "distilled from detailed Findings." This paper proposes a novel prompting strategy that enhances RRS by introducing a layperson summary as an intermediate step. This summary helps normalize key observations and simplify complex terminology using communication techniques inspired by doctor–patient interactions. Combined with few-shot in-context learning, this approach improves the model’s ability to map generalized descriptions to specific clinical findings. We evaluate our method on three benchmark datasets, MIMIC-CXR, CheXpert, and MIMIC-III, and compare it against state-of-the-art open-source language models in the 7B/8B parameter range, such as Llama-3.1-8B-Instruct. Results show consistent improvements in summarization quality, with gains of up to 5% on some metrics for prompting, and more than 20% for some models when instruction tuning.