Sensor-based applications, such as smart homes, require prediction of event occurrences for automating the environment using time-series data collected over a period of time. In these applications, it is important to predict events in tight and accurate intervals to effectively automate the application. This article deals with the discovery of significant intervals from time-series data. Although there is a considerable body of work on sequential mining of transactional data, most of them deal with time-point data and make several passes over the entire data set in order to discover frequently occurring patterns/events. We propose an approach in which significant intervals representing intrinsic nature of data are discovered in a single pass. In our approach, time-series data is folded over a periodicity (day, week, etc.) in which the intervals are formed. Significant intervals are discovered from this interval data that satisfy the criteria of minimum confidence and maximum interval length specified by the user. Both compression and working with intervals contribute towards improving the efficiency of the algorithm. In this article, we present a new single-pass algorithm for detecting significant intervals; discuss its characteristics, advantages, and disadvantages; and analyze it. Finally, we compare the performance of our algorithm with previously developed level-wise and SQL-based algorithms for significant interval discovery (SID).