Pocock (1977), O'Brien & Fleming (1979) and Slud & Wei (1982) have proposed different methods to construct discrete sequential boundaries for clinical trials. These methods require that the total number of decision times be specified in advance. In the present paper, we propose a more flexible way to construct discrete sequential boundaries. The method is based on the choice of a function, α*(t), which characterizes the rate at which the error level α is spent. The boundary at a decision time is determined by α*(t), and by past and current decision times, but does not depend on the future decision times or the total number of decision times.