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Software testing is a crucial but time-consuming aspect of software development, and recently, Large Language Models (LLMs) have gained popularity for automated test case generation. However, because LLMs are trained on vast amounts of open-source code, they often generate test cases that do not adhere to best practices and may even contain test smells (anti-patterns). To address this issue, we propose Reinforcement Learning from Static Quality Metrics (RLSQM), wherein we utilize Reinforcement Learning to generate high-quality unit tests based on static analysis-based quality metrics. First, we analyzed LLM-generated tests and show that LLMs frequently do generate undesirable test smells -- up to 37% of the time. Then, we implemented lightweight static analysis-based reward model and trained LLMs using this reward model to optimize for five code quality metrics. Our experimental results demonstrate that the RL-optimized Codex model consistently generated higher-quality test cases than the base LLM, improving quality metrics by up to 23%, and generated nearly 100% syntactically-correct code. RLSQM also outperformed GPT-4 on all code quality metrics, in spite of training a substantially cheaper Codex model. We provide insights into how reliably utilize RL to improve test generation quality and show that RLSQM is a significant step towards enhancing the overall efficiency and reliability of automated software testing. Our data are available at https://doi.org/10.6084/m9.figshare.25983166.