The median confidence interval is useful for one parameter families, such as the exponential distribution, and it may not need to be adjusted if censored observations are present. In this article, two estimators for the median of the exponential distribution, MD, are considered and compared based on the sample median and the maximum likelihood method. The first estimator is the sample median, MD1, and the second estimator is the maximum likelihood estimator of the median, MDMLE. Both estimators are used to propose a modified confidence interval for the population median of the exponential distribution, MD. Monte Carlo simulations were conducted to evaluate the performance of the proposed confidence intervals with respect to coverage probability, average width and standard error. A numerical example using a real data set is employed to illustrate the use of the modified confidence intervals; results are shown.