The objective of this paper is to demonstrate a new capability to detect faint stratospheric aerosols in atmospheric lidar data from NASA’s Cloud-Aerosol Lidar Infrared Pathfinder Satellite Observations (CALIPSO) Mission (12 June 2006 30 June 2023) at high resolution. Faint aerosols from wildfires, distant volcanic eruptions, and Asian and Saharan dust storms play important roles in the Earth-Atmosphere system, as they provide essential air quality and pollution, airline safety, climate radiative forcing, monitoring of fires and volcanic eruptions, environmental safety, and weather forecasting. Tenuous aerosols are recorded in the CALIOP atmospheric lidar data from the CALIPSO mission, but especially extremely faint stratospheric aerosol layers often escape detection and classification partly or entirely in the current CALIOP data analysis scheme. To solve this problem, we introduce a new algorithm for detection and height determination of atmospheric layers, the Density-Dimension Algorithm for CALIOP data analysis (CALIOP-DDA). The DDA is an auto-adaptive algorithm that builds on concepts from artificial intelligence and spatial statistics. Core steps are calculation of a density field and application of a threshold function for signal-noise separation. Stratospheric aerosol detection is aided by the tropopause split concept. The CALIOP-DDA facilitates detection of extremely faint stratospheric aerosols from various sources, including distant wildfires and volcanic eruptions, in nighttime and day-time CALIOP data, even in presence of complex types of other cloud and aerosol layers across a large range of optical thicknesses, while retaining the full 334m along-track, 30m height resolution, without creating false positives. CALIOPDDA results are evaluated by comparison to layer heights derived from airborne validation experiments, conducted using the Cloud Physics Lidar (CPL). In conclusion, the CALIOP-DDA holds promise as the algorithmic basis for a future improved, high-resolution CALIPSO data product.