Rapidly increasing model scales coupled with steering methods such as chain-of-thought prompting have led to drastic improvements in language model reasoning. At the same time, models struggle with compositional generalization and are far from human performance on many reasoning-based benchmarks. Leveraging the success of chain-of-thought prompting, and also taking inspiration from context-aware decoding (CAD), we explore input-based contrasting methods to further encourage the type of reasoning induced by chain-of-thought prompting. While work remains to stabilize these results across datasets and models, the improvements we find warrant further investigation into input-based steering methods for context-aware reasoning.