Agentic Test-Time Scaling (TTS) has delivered state-of-the-art (SOTA) performance on complex software engineering tasks such as code generation and bug fixing. However, its practical adoption remains limited due to significant computational overhead, primarily driven by two key challenges: (1) the high cost associated with deploying excessively large ensembles, and (2) the lack of a reliable mechanism for selecting the optimal candidate solution, ultimately constraining the performance gains that can be realized. To address these challenges, we propose Entropy-Guided Stepwise Scaling (EGSS), a novel TTS framework that dynamically balances efficiency and effectiveness through entropy-guided adaptive search and robust test-suite augmentation. Extensive experiments on SWE-Bench-Verified demonstrate that EGSS consistently boosts performance by 5-10% across all evaluated models. Specifically, it increases the resolved ratio of Kimi-K2-Intruct from 63.2% to 72.2%, and GLM-4.6 from 65.8% to 74.6%. Furthermore, when paired with GLM-4.6, EGSS achieves a new state-of-the-art among open-source large language models. In addition to these accuracy improvements, EGSS reduces inference-time token usage by over 28% compared to existing TTS methods, achieving simultaneous gains in both effectiveness and computational efficiency.