Central counterparties (CCPs) are designed to withstand the simultaneous default of their largest two clearing members in extreme but plausible market conditions. In very extreme cases, it is nonetheless possible that default losses exceed the available resources. Then, the CCP generally has two recovery tools available for loss allocation: assessments (also known as cash calls) and variation margin gains haircutting (VMGH). Generally, the application of the standard CCP waterfall rules can absorb all default losses (ie, achieve full loss allocation) using assessments and VMGH, provided there is no regulatory intervention on systemic risk grounds by a CCP resolution authority. However, the systemic impacts of the two loss allocation recovery tools may be very different. Assessments charge each clearing member an amount proportional to its contribution to the default fund, which is risk-based and known in advance of the default event. In contrast, VMGH charges those clearing members that happen to have an overall portfolio that was worth more at the moment of default than at the last mark-to-market valuation. The profit or loss of a whole portfolio changes from moment to moment with changing market prices and the novation of new contracts. From a systemic risk perspective it is therefore beneficial if VMGH can be avoided altogether. The aim of this paper is to assess the circumstances under which a CCP can absorb the default of up to n clearing members without resorting to VMGH.