For a one-parameter negative exponential population, reasonably good interval estimates of the parameter σ may be obtained from one suitably chosen order statistic. The coefficients of themth order statisticxmin exact confidence bounds for σ are found by taking the negative reciprocals of the natural logarithms of percentage points of the Beta distribution. The interval between exact lower and upper confidence bounds, each associated with confidence 1 –P, is, of course, an exact central confidence interval (confidence 1 – 2P). Results have been computed for several values ofm, clustered about the value which yields the most efficient point estimator, for sample sizen= 1(1)20(2)40 andP= .0001, .0005, .001, .005, .01, .025, .05, .1(.1).5. The definition of efficiency commonly used for point estimators is extended to confidence bounds and confidence intervals. The following tables are included, together with a description of the method of computation and a brief discussion of possible uses: (1) a table of upper confidence bounds and central confidence intervals for σ, based on one order statistic, together with their efficiencies, for that value ofmwhich maximizes the efficiency of the upper confidence bound, for each combination ofnand 1 –Pand (2) a similar table for that value ofmwhich maximizes the efficiency of the central confidence interval, when the two values ofmdiffer. A numerical example is also given.