The fundamental purpose of an emissions trading system (ETS) is to constrain emissions and enable the market to set an emissions price path that facilitates an effective transition to a low-emissions economy. In a conventional ETS, the emissions constraint is defined by a cap (a fixed limit) on tradable, government-issued emission units together with a quantity limit on any external units allowed in the system (e.g. via an offsets mechanism). Essentially, an ETS cap underpins the ambition, cost-effectiveness, distributional implications, and credibility of a jurisdiction’s approach to decarbonisation. From 2008 to mid-2015, the New Zealand Emissions Trading Scheme (NZ ETS) broke from convention by linking to the global Kyoto cap without its own limit on domestic emissions. NZ ETS participants met compliance obligations using unlimited overseas units at low prices and faced little incentive to reduce their own emissions. The NZ ETS delinked from the Kyoto market in mid-2015, creating uncertainty over the future of domestic unit supply and an efficient price path for domestic decarbonisation. This working paper, which evolved under Motu’s ETS Dialogue process from 2016 to 2018, explores key considerations for ETS cap setting and proposes the design for a cap on units auctioned and freely allocated in the NZ ETS. The recommendations focus on issues of cap architecture rather than ambition. The proposed cap is defined in tonnes of emissions per year, fixed for five years in advance, extended by one year each year, and guided by an indicative ten-year cap trajectory. The fixed cap and cap trajectory need to reflect consideration of New Zealand’s domestic decarbonisation objectives, international targets, mitigation potential and costs in both ETS and non-ETS sectors, and prospects for cost-effective investment in overseas emission reductions. Two companion working papers address how the choice of cap will interact with decisions on ETS price management mechanisms and linking to overseas markets. The three working papers elaborate on an integrated proposal for managing unit supply, prices, and linking in the NZ ETS that was presented in Kerr et al. (2017).