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The increasing share of distributed energy sources enhances the participation potential of distributed flexibility in the provision of system services. However, this participation can endanger the grid-safety of the distribution networks (DNs) from which this flexibility originates. In this paper, the use of operating envelopes (OE) to enable the grid-safe procurement of distributed flexibility in centralized balancing markets is proposed. Two classes of approaches for calculating OEs (one-step and two-step methods) are compared in terms of the level of distribution grid safety they can provide, the impact they can have on the market efficiency, and the volume of discarded flexibility they can yield. A case study considering different system scenarios, based on Monte Carlo simulations, highlights a trade-off between the market efficiency, DN flexibility resource utilization, and the grid safety delivered by the different OE methods. The results showcase that the use of the two-step OE approach results in a more grid-secure albeit less-efficient use of distributed flexibility., Comment: 5 pages