The efficiency of the directed-priming proposal of Studier [Proc. Natl. Acad. Sci. USA 86 (1989) 6917-1921] can be improved upon by employing a library of less than 4094 hexamers, allowing for the easy construction of all required primers using template-directed automated ligation. This 'top-down' sequencing procedure should be several times more efficient than the present 'bottom-up' procedures [see Watson, Science 248 (1990) 44-49].