Balancing high performance with interpretability in increasingly powerful Transformer-based models remains a challenge. While mechanistic interpretability aims to specify neural network computations in explicit, pseudocode-like formats, existing methods often involve laborious manual analysis or struggle to fully elucidate learned internal algorithms. Recent efforts to build intrinsically interpretable models have introduced considerable expressivity and optimization challenges. This work introduces Adaptive Transformer Programs, an enhanced framework building upon RASP language and Transformer Programs to create more robust and interpretable models. The proposed method increases expressivity by redesigning two primary attention modules to improve categorical and numerical reasoning capabilities. To overcome optimization hurdles, we introduce a novel reparameterization scheme that enhances the exploration-exploitation trade-off during training. We validate our approach through extensive experiments on diverse tasks, including in-context learning, algorithmic problems (e.g., sorting and Dyck languages), and NLP benchmarks such as named entity recognition and text classification. Results demonstrate that Adaptive Transformer Programs substantially narrow the performance gap between black-box Transformers and interpretable models, enhancing transparency. This work advances the development of high-performing, transparent AI systems for critical applications, addressing crucial ethical concerns in AI development.