Scaling up neural networks has been a key recipe to the success of large language and vision models. However, in practice, up-scaled models can be disproportionately costly in terms of computations, providing only marginal improvements in performance; for example, EfficientViT-L3-384 achieves <2% improvement on ImageNet-1K accuracy over the base L1-224 model, while requiring $14\times$ more multiply-accumulate operations (MACs). In this paper, we investigate scaling properties of popular families of neural networks for image classification, and find that scaled-up models mostly help with "difficult" samples. Decomposing the samples by difficulty, we develop a simple model-agnostic two-pass Little-Big algorithm that first uses a light-weight "little" model to make predictions of all samples, and only passes the difficult ones for the "big" model to solve. Good little companion achieve drastic MACs reduction for a wide variety of model families and scales. Without loss of accuracy or modification of existing models, our Little-Big models achieve MACs reductions of 76% for EfficientViT-L3-384, 81% for EfficientNet-B7-600, 71% for DeiT3-L-384 on ImageNet-1K. Little-Big also speeds up the InternImage-G-512 model by 62% while achieving 90% ImageNet-1K top-1 accuracy, serving both as a strong baseline and as a simple practical method for large model compression.