Output-based allocation (OBA) is one of the main options discussed for address- ing carbon leakage in emissions trading systems. This paper studies how different OBA designs affect incentives on mitigation and trade in the cement sector. To do so, we develop an analytical model of sector emissions as a function of technical parameters representing abatement levers. We propose a specific design called hybrid OBA, and show that unlike the alternatives, it provides incentives for firms to reduce the carbon intensity of produc- tion without offshoring production. We assess the feasibility of hybrid OBA through expert interviews and find that the main barriers identified, including technical and administrative complexities, are manageable. However, hybrid OBA represents a mid-term solution until more robust anti-leakage measures can be introduced, because of two key limitations of OBA in general - it does not provide incentives to reduce the consumption of cement or to accelerate the development of radical low-carbon technologies, both of which are necessary to deliver deep decarbonisation.