This paper presents a study on the computational complexity of coding for machines, with a focus on image coding for classification.We first conduct a comprehensive set of experiments to analyze the size of the encoder (which encodes images to bitstreams), the size of the decoder (which decodes bitstreams and predicts class labels), and their impact on the rate-accuracy trade-off in compression for classification.Through empirical investigation, we demonstrate a complementary relationship between the encoder size and the decoder size, \ie, it is better to employ a large encoder with a small decoder and vice versa.Motivated by this relationship, we introduce a feature compression-based method for efficient image compression for classification.By compressing features at various layers of a neural network-based image classification model, our method achieves adjustable rate, accuracy, and encoder (or decoder) size using a single model.Experimental results on ImageNet classification show that our method achieves competitive results with existing methods while being much more flexible.The code will be made publicly available.