Periodic as well as annual stochastic streamflow models have been fitted to the highly variable flows measured at Krishnarajasagara (KRS) on river Cauvery (Southern India), which is monsoon-dependent and hence prone to drought. Based on 100 synthetic flow sequences generated from each model, the preservation of over-year drought characteristics is compared, for three truncation levels and four return periods. The method used to find out the drought characteristics is after Wang and Salas (1989). The study shows that the periodic models explicitly designed to preserve the periodic correlations are able to preserve the drought durations consistently well, but not the deficit sum; whereas simple models namely, annual autoregressive model of order one (AR(1)) and Thomas-Fiering lognormal 3-parameter monthly model are able to preserve the deficit sum better than the periodic models, even though they have not been able to reproduce the basic historical flow statistics at the verification stage. On the other hand, the Gamma autoregressive model of order one (GAR(1) with bias corrections), does very well at the verification stage, but fails to reproduce the drought characteristics. However, none of the stochastic models fitted is able to preserve critical historical drought durations for high return periods.