Discrete speech units (DSUs) are derived from clustering the features of self-supervised speech models (S3Ms). DSUs offer significant advantages for on-device streaming speech applications due to their rich phonetic information, high transmission efficiency, and seamless integration with large language models. However, conventional DSU-based approaches are impractical as they require full-length speech input and computationally expensive S3Ms. In this work, we reduce both the attention window and the model size while preserving the effectiveness of DSUs. Our results demonstrate that we can reduce floating-point operations (FLOPs) by 50% with only a relative increase of 6.5% in character error rate (CER) on the ML-SUPERB 1h dataset. These findings highlight the potential of DSUs for real-time speech processing in resource-constrained environments.