This paper introduces a parameterization framework for controlling conversation quality in large language models. We explore nine key parameters across six dimensions that enable precise specification of dialogue properties. Through experiments with state-of-the-art LLMs, we demonstrate that parameter-based control produces statistically significant differences in generated conversation properties. Our approach addresses challenges in conversation generation, including topic coherence, knowledge progression, character consistency, and control granularity. The framework provides a standardized method for conversation quality control with applications in education, therapy, customer service, and entertainment. Future work will focus on implementing additional parameters through architectural modifications and developing benchmark datasets for evaluation.