The current document is directed to a multi-stage metric-data compression method and subsystem for compressing metric data collected and stored within distributed computing systems to facilitate computer-system management and administration. In a described implementation, metric data is partitioned into constant metric data, low-variability metric data, and high-variability metric data. High-variability metric data is compressed by identifying a set of basis metrics, or independent metrics, with respect to which a remaining set of dependent metrics can be expressed using coefficient multipliers. The high-variability metric data can then be stored as a set of independent metrics and set of coefficients, along with a small amount of additional data.