In predictive image coding, the least squares (LS)-based adaptive predictor is noted as an efficient method to improve prediction result around edges. However pixel-by-pixel optimization of the predictor coefficients leads to a high coding complexity. To reduce computational complexity, we activate the LS optimization process only when the coding pixel is around an edge or when the prediction error is large. We propose a simple yet effective edge detector using only causal pixels. The system can look ahead to determine if the coding pixel is around an edge and initiate the LS adaptation to prevent the occurrence of a large prediction error. Our experiments show that the proposed approach can achieve a noticeable reduction in complexity with only a minor degradation in the prediction results.