General-purpose Large Language Models (LLMs) are frequently fine-tuned through supervised fine-tuning (SFT) to enhance performance in specific domains. Better results can be achieved by distilling the chain-of-thought of a larger model at the cost of numerous expensive calls and a much greater amount of data.We propose a novel blueprint for efficient fine-tuning that uses reasoning only for complex data identified by entropy. Specifically, across three small open models (≈ 3B) we split the training data into complexity categories by a single token answer entropy (ROC AUC 0.73), fine-tune large language models (LLMs) via SFT and distillation, and show that our pipeline significantly outperforms the standard SFT approach (0.58 vs 0.45 average accuracy) and outperforms the distillation approach (0.58 vs 0.56 average accuracy) while using 81% less data.We publish our code and data to facilitate further research in this direction.