This paper discusses a new piecewise exponential estimator (NPEE) of a survival function
(SF) for censored data, which is continuous on 
. For comparison purposes, we consider
the Kaplan-Meier estimator (KME) and the empirical Bayes type estimator (EBE)
derived by Rai et al. (1980). The EBE estimate beyond the last observation is determined
solely by the prior. The NPEE retains the spirit of the KME and provides an exponential
tail with a hazard rate determined by a novel nonparametric consideration. The NPEE has
been compared with the KME and EBE for small sample sizes by simulation. The simulation
comparisons are by the measures of bias and three norms, 
, for
three levels of censoring, (15\%, 50\%, 75\%), and two sample sizes (10 and 30). Generally
speaking, the NPEE, which is asymptotically equivalent to the KME (Malla and Mukerjee
(2010)), seems to be better than the KME, especially when we have heavy censoring and/or
small sample sizes, and is at least as good as the EBE.