Stimulated Raman scattering (SRS) from micrometer-sized droplets, which results from coupling of spontaneous Raman emission to droplet morphology-dependent resonances (MDR's), exhibits unique characteristics. Spatial patterns consist of bright SRS arcs on the droplet rim. A second source of SRS emission has recently been observed from a ringlike region encircling the droplet axis near the geometric focus (the Descartes ring). Investigation of the time and spectral characteristics of Descartes ring SRS and its suppression by the addition of absorptive dye to the droplet reveals it to be an additional manifestation of droplet MDR's. We conjecture that the Descartes ring results when the MDR light is scattered by refractive-index inhomogeneities produced by the intense pump field within the droplet.