The dependence of the initial rate of introduction of the first single-chain scission (initial nicking rate) into covalently closed circular phage PM2 DNA by the single strand-specific nuclease from Alteromonas espejiana BAL 31 upon the superhelix density (sigma) of the DNA has been examined. The initial nicking rate decreases with decreasing numbers of negative superhelical turns (decreasing values of -sigma), which behavior is characteristic of other single strand-specific nucleases as reported earlier. In contrast to earlier work, the initial nicking rates of closed circular DNAs by the action of the Alteromonas nuclease have been shown to be readily measurable at values of -sigma as low as 0.02. However, even at the elevated concentrations of enzyme and extended digestion periods required to cause nicking at an appreciable rate at near-zero values of sigma, closed circular DNA containing very few superhelical turns (form IO DNA) is not cleaved at a detectable rate. When this DNA is rendered positively supercoiled by ethidium bromide (EtdBr), it is not affected by the nuclease until very high positive values of sigma are attained, at which low rates of cleavage can be detected at elevated enzyme concentrations. The effects of EtdBr on the enzyme activity have been tested and are entirely insufficient to allow the interpretation of zero nicking rates as the result of inhibition of the nuclease activity by the dye. Positively supercoiled DNA is concluded not to contain regions having significant single-stranded character until values of sigma are reached which are very much higher than the values of -sigma for which negatively supercoiled DNAs behave as if they contain unpaired or weakly paired bases.