In certain situations in life testing, it is more practical to record whether a unit fails in an interval instead of measuring failure times exactly. This paper considers the analysis of life data from the exponential distribution with the use of periodic monitoring. A number of different monitoring schemes are presented and compared. We show that when it is not feasible to record every measurement exactly, the use of as few as two strategically selected monitoring times can be used to analyze the data with only a moderate loss in efficiency for certain problems. The paper also presents sampling plans for a lower-tailed test for the mean of an exponential distribution using two monitoring times. Although the paper focuses on the exponential distribution, all the results also hold for a Weibull distribution with a known shape parameter.