Dielectric spectroscopy measurements were performed for aqueous solutions of short single-stranded DNA with 30 to 120 bases of thymine over a frequency range of 10;{5} to 10;{8}Hz . Dielectric dispersion was found to include two relaxation processes in the ranges from 10;{5} to 10;{6} and from 10;{6} to 10;{8}Hz , respectively, with the latter mainly discussed in this study. The dielectric increment and the relaxation time of the high-frequency relaxation of DNA in solutions without added salt exhibited concentration and polymer-length dependences eventually identical to those for dilute polyion solutions described in previous studies. For solutions with added salt, on the other hand, those dielectric parameters were independent of salt concentration up to a certain critical value and started to decrease with further increasing salt concentration. This critical behavior is well explained by our newly extended cell model that takes into account the spatial distribution of loosely bound counterions around DNA molecules as a function of salt concentration.