We have developed two systems, FN and ANDD, that use natural language and graphical displays, respectively, to communicate information about objects to human users. Both systems must deal with the fundamental problem of ensuring that their output does not carry unwanted and inappropriate conversational implicatures. We describe the types of conversational implicatures that FN and ANDD can avoid, and the computational strategies the two systems use to generate output that is free of unwanted implicatures.