This paper introduces a new method for reducing the number of distance calculations in the generalized Lloyd algorithm (GLA), which is a widely used method to construct a codebook in vector quantization. Reduced comparison search detects the activity of the code vectors and utilizes it on the classification of the training vectors. For training vectors whose current code vector has not been modified, we calculate distances only to the active code vectors. Large proportion of the distance calculations can be omitted without sacrificing the optimality of the partition. The new method is included in several fast GLA variants reducing their running times over 50% on average.