The supply of allowances in the European Union Emissions Trading System is determined within a rigid allocation programme. A reform of the EU ETS intends to make allowances allocation exible and contingent on the state of the system. We model the emissions market under adjustable allowance supply in a stochastic partial equilibrium framework and obtain closed form solutions for its dynamics. The model considers a supply control mechanism contingent on the number of allocated and unused allowances, as suggested by the European Commission. We derive analytical dependencies between the allowance allocation adjustment rate and the market equilibrium dynamics, which allows us to represent the quantity thresholds as quantiles for the number of allocated and unused allowances. Finally, we present an analytical tool for the selection of an optimal adjustment rate under both risk-neutrality and risk-aversion. We thereby provide an analytical foundation for the regulator's decision-making in the context of the EU ETS reform and give a novel perspective on the mechanism's overall design.