Lambda exonuclease processively degrades one strand of duplex DNA, moving 5'-to-3' in an ATP-independent fashion. When examined at the single-molecule level, the speeds of digestion were nearly constant at 4 nanometers per second (12 nucleotides per second), interspersed with pauses of variable duration. Long pauses, occurring at stereotypical locations, were strand-specific and sequence-dependent. Pause duration and probability varied widely. The strongest pause, GGCGAT TCT, was identified by gel electrophoresis. Correlating single-molecule dwell positions with sequence independently identified the motif GGCGA. This sequence is found in the left lambda cohesive end, where exonuclease inhibition may contribute to the reduced recombination efficiency at that end.