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The present paper proposes a novel method for computing inter-domain paths subject to multiple independent additive constraints in MPLS-TE networks. An efficient solution to this problem is a key element for providing services with guaranteed performance across domain boundaries. However, the inherent hardness of the multi-constrained path computation as well as inter-domain scalability and security constraints complicate the computation problem. We propose a novel algorithm named kID-MCP that tackles the computational complexity of the problem by reducing the number of paths included in the computation process. kID-MCP is compatible with existing techniques and fulfills the security requirements. We undergo a complexity analysis that shows that kID-MCP scales well. Moreover, a simulation study reveals that kID-MCP finds a solution in most situations. These results indicate that the computation of inter-domain multi-constrained paths is tractable in practice, which opens interesting perspectives for QoS routing and traffic engineering among multiple operators.