The long-tailed image classification task remains important in the development of deep neural networks as it explicitly deals with large imbalances in the class frequencies of the training data. While uncommon in engineered datasets, this imbalance is almost always present in real-world data. Previous approaches have shown that combining cross-entropy and contrastive learning can improve performance on the long-tailed task, but they do not explore the tradeoff between head and tail classes. We propose a novel class instance balanced loss (CIBL), which reweights the relative contributions of a cross-entropy and a contrastive loss as a function of the frequency of class instances in the training batch. This balancing favours the contrastive loss for more common classes, leading to a learned classifier with a more balanced performance across all class frequencies. Furthermore, increasing the relative weight on the contrastive head shifts performance from common (head) to rare (tail) classes, allowing the user to skew the performance towards these classes if desired. We also show that changing the linear classifier head with a cosine classifier yields a network that can be trained to similar performance in substantially fewer epochs. We obtain competitive results on both CIFAR-100-LT and ImageNet-LT.