Long chain-of-thought (CoT) prompting helps Large Language Models (LLMs) solve difficult problems, but very long traces often slow or even degrade performance on fast, intuitive "System-1" tasks. We introduce Connector-Aware Compact CoT (CAC-CoT) -- a method that deliberately restricts reasoning to a small, fixed set of connector phrases, steering the model toward concise and well -- structured explanations. Despite its simplicity, our synthetic method with general-purpose LLMs yields a high-quality training quality. CAC-CoT achieves approximately 85% on GSM8K and approximately 40% on GPQA (System-2) while also achieving approximately 85% on S1-Bench (System-1), surpassing the baseline by over 20%. Its reasoning traces average approximately 300 tokens(ART), about one-third the length of baseline traces, delivering higher efficiency without loss of accuracy.