Basic narrowing is known to be adequate for solving equations with respect to 
an equational theory E, when E admits a finite canonical rewrite system. If 
E is not so well-behaved, one may still combine ordered completion with basic 
narrowing, to deduce a complete procedure for E-unification. The situaion is 
unexpectedly lore complicated when we try to combine ordered basic completion 
with basic narrowing : the lemma of Hullot ceases to be true in its usual 
form. The objective of this paper is to show that such a combination of basic 
narrowing and ordered basic completion does exist, and provides a complete 
tool for E-unification. This is obtained via an inference system covering 
both ordered completion and narrowing ina setup of constrained rewriting, 
which is an appropriate formalism for expressing the basic character of both. 
Initial equations with equlity or ordering constraints are allowed; our 
approach also incorporates sufficiently many simplification steps so as to be 
able to provide 'basic' canonical systems for all classical examples (e.g. 
groups).