Transparency and openness are broadly endorsed in energy and environmental modelling and analysis, but too little attention is given to the transparency of value-laden assumptions. Current practices for transparency focus on making model source code and data available, documenting key equations and parameter values, and ensuring replicability of results. We argue that, even when followed, these guidelines are insufficient for achieving deep transparency, in the sense that results often remain driven by implicit value-laden assumptions that are opaque to other modellers (...) and researchers, and that may not be understood by wider audiences to be controversial. This paper identifies additional best practices for achieving transparency by highlighting issues where disagreement over value judgements will persist for the foreseeable future. Recommendations for deepening transparency are developed by learning from successes and ongoing challenges represented in three case studies. We provide recommendations to accelerate the adoption of additional best practices for deepening transparency of energy and environmental modelling in policy-relevant domains, increasing stakeholder participation with non-modellers, and encouraging interdisciplinary dialogue. (shrink)