The ability to compute shortest constrained Traffic Engineering Label Switched Paths (TE LSPs) in Multiprotocol Label Switching (MPLS) and Generalized MPLS (GMPLS) networks across multiple domains has been identified as a key requirement. In this context@ a domain is a collection of network elements within a common sphere of address management or path computational responsibility such as an IGP area or an Autonomous Systems. This document specifies a procedure relying on the use of multiple Path Computation Elements (PCEs) to compute such inter-domain shortest constrained paths across a predetermined sequence of domains@ using a backward-recursive path computation technique. This technique preserves confidentiality across domains@ which is sometimes required when domains are managed by different service providers.