This paper concerns software support for non-blocking transactions in shared-memory multiprocessors. We present mechanisms that convert sequential transactions into lock-free or wait-free ones. In contrast to some previous mechanisms, ours support transactions for which the set of memory locations accessed cannot be determined in advance. Our implementations automatically detect and resolve conflicts between concurrent transactions, and allow transactions that do not conflict to execute in parallel. The key to the efficiency of our wait-free implementation lies in using a lock-free (but not wait-free) multi-word compare-and-swap (MWCAS) operation. By introducing communication between a high-level helping mechanism and the lock-free MWCAS, we show that an expensive wait-free MWCAS is not necessary to ensure wait-freedom.