The current document is directed to methods and systems that collect metric data within computing facilities, including large data centers and cloud-computing facilities. In a described implementation, input metric data is compressed by replacing each metric data point with a one-bit, two-bit, four-bit, or eight-bit compressed data value. During a first time window following reception of a metric data point, the metric data point remains available in uncompressed form to facilitate data analysis and monitoring functionalities that use uncompressed metric data. During a second time window, the metric data point is compressed and stored in memory, where the compressed data point remains available for data analysis and monitoring functionalities that use compressed metric data for detection of peaks, periodic patterns, and other characteristics. Finally, the compressed data point is archived in mass storage, where it remains available to data-analysis and management functionalities for a lengthy time period.