In this study, we aim to enhance radiology reporting by improving both the conciseness and structured organization of findings (also referred to as templating), specifically by organizing information according to anatomical regions. This structured approach allows physicians to locate relevant information quickly, increasing the report's utility. We utilize Large Language Models (LLMs) such as Mixtral, Mistral, and Llama to generate concise, well-structured reports. Among these, we primarily focus on the Mixtral model due to its superior adherence to specific formatting requirements compared to other models. To maintain data security and privacy, we run these LLMs locally behind our institution's firewall. We leverage the LangChain framework and apply five distinct prompting strategies to enforce a consistent structure in radiology reports, aiming to eliminate extraneous language and achieve a high level of conciseness. We also introduce a novel metric, the Conciseness Percentage (CP) score, to evaluate report brevity. Our dataset comprises 814 radiology reports authored by seven board-certified body radiologists at our cancer center. In evaluating the different prompting methods, we discovered that the most effective approach for generating concise, well-structured reports involves first instructing the LLM to condense the report, followed by a prompt to structure the content according to specific guidelines. We assessed all prompting strategies based on their ability to handle formatting issues, reduce report length, and adhere to formatting instructions. Our findings demonstrate that open-source, locally deployed LLMs can significantly improve radiology report conciseness and structure while conforming to specified formatting standards.