Designing a DL system poses the problem of the trade-o between power of expression and complexity. In spite of their rich expressive capacity, the or and not constructors are usually avoided because of the intractability of the resulting subsomption algorithm. So is implication. However, implication may constitute an interesting compromise between expressive power andtractability. Wepresent anapproach to the treatment of implication in the Osiris system, for mono-valued attributes with enumerated domains. It is based on the partitioningof each attribute's domainby the predicates on this attribute, and it has been implemented in a prototype version of the Osiris system.