What is the common law power of the police to search a lawfully arrested person?

The police have a common law power to search a lawfully arrested person: Cloutier v. Langlois, 1990 CanLII 122 (SCC), [1990] 1 S.C.R. 158, 74 C.R. (3d) 316, 53 C.C.C. (3d) 257. The power to search incident to arrest does not depend on the existence of reasonable and probable grounds. However, as L’Heureux-Dubé J. explained at p. 278 C.C.C of that unanimous decision, there are limits to the power to search incident to arrest: The power to search does not impose a duty. The police have some discretion in conducting the search . . . The search must be for a valid objective in pursuit of the ends of criminal justice, such as the discovery of an object that may be a threat to the safety of the police, the accused or the public, or that may facilitate escape or act as evidence against the accused. . . . The search must not be conducted in an abusive fashion and, in particular, the use of physical or psychological constraint should be proportionate to the objectives sought and other circumstances of the situation.