Pulsed, visible and near-infrared laser light is coupled into an optical fiber, which is wound into a loop using a fiber splice connector. The light pulses traveling through the fiber-loop are detected using a photomultiplier detector. It is found that once the light is coupled into the fiber it experiences very little loss and the light pulses do a large number of round trips before their intensity is below the detection threshold. Measurements of the loss-per-pass and of the ring-down time allow for characterization of the different loss mechanisms of the light pulses in the fiber and splice connector. This method resembles "cavity ring-down absorption spectroscopy" and is well suited to characterize low-loss processes in fiber optic transmission independent from power fluctuations of the light source. It is demonstrated that by measuring the ring-down times one can accurately determine the absolute transmission of an optical fiber and of the fiber connector. In addition it is demonstrated that the technique is useful as an absorption spectroscopic technique of very small sample volumes. A solution of an organic dye was placed between the fiber ends instead of the usual index matching fluid, and an absorption spectrum of 7x10(-15) mol of the dye 1,1(')-diethyl-4,4(')-dicarbocyanine iodide in 7x10(-12) L of dimethylsulfoxide was recorded.