Ongoing tests involving the application of double optical feedback to a vertical-cavity surface-emitting laser (VCSEL) are resulting in demonstrable and significant improvements in oscillation linewidth and frequency stability. We look into the workings of a double optical feedback system for a Fabry-Pérot-type diode laser. We describe a single-mode VCSEL that is characterized by a narrow oscillation linewidth and a stable output intensity that shows no trace of the low-frequency fluctuation (LFF) that so often occurs in single optical feedback diode lasers. Initial tests use a beat note to do this. From there, we calculate the square root of the Allan variance to determine the level of frequency stability. We also evaluate the degree of LFF suppression achieved using its spectrum density and compare those results with what we obtained through single and double optical feedback and with no feedback whatsoever.