The framework for carbon removal obligations (CROs), introduced in ref1, consists of two core mechanisms: (1) the principal CRO mechanism obliges the emitter of a tonne of CO2 to remove a tonne of CO2 from the atmosphere at maturity of the CRO; and (2) the CRO pricing instrument imposes a premium (‘CRO Premium’) on carbon debt, defined as the emissions overshooting the remaining carbon budget. The CRO Premium thus adjusts carbon price levels induced by the principal CRO mechanism to alter the emission profile according to some prespecified preferences. This technical working paper amends and extends the analytical CRO model in two fundamental ways: (1) instead of net emissions we consider gross emissions as basis for carbon debt creation, and gross removals for its compensation. This extends the scope of the principal CRO mechanism and is the basis for disentangling the emission trading system (ETS), that ref1 relies on, from the CDR market; and (2) we introduce the methodology defining the CRO Premium. We deploy the updated analytical framework using a simple numerical model to compute a set of illustrative climate mitigation pathways. Along these scenarios we assess the potential benefits from setting separate targets for emissions reductions and carbon removals – a possibility that results from the disentanglement of the ETS and the CDR market.