Pragma-dialectics is dynamic, context-sensitive, and multi-agent; it promises theories of fallacy and argumentative structure. But pragma-dialectic theory and practice are not yet fully in harmony. Key definitions of the theory fall short of explicating the analyses that pragma-dialecticians actually do. Many discussions involve more than two participants with different and mutually incompatible standpoints. Success in such a discussion may be more than success against each opponent. Pragma-dialectics does well at analyzing arguments advanced by one party, directed at another party; it (...) does much less well at analyzing arguments directed at several opponents at once or at convincing an audience. I suggest a strategy of construing fallacies as defeasible arguments relying on reasonable default principles but applying them in circumstances in which they are undercut or overridden. (shrink)