Saturated absorption spectroscopy linewidths down to half the natural linewidth have been obtained for the sodium D 1 transition in a strongly absorbing gas cell. The strong-line-narrowing effect is achieved by using an experimental ''tandem'' approach with two absorbing cells in series, where the saturated absorption output from the first cell is used as an input beam for a saturated absorption measurement in the second cell. A physical interpretation of the line-narrowing mechanism in highly absorbing media is presented, which, among other things, explains why the narrowing effects are different for crossover transitions. It is further argued that in these experiments the line-narrowing effect is caused by optical pumping and can be appropriately described by rate equations. This is different from several other recent papers on high-contrast transmission spectroscopy, where full Bloch vector models were necessary to fully describe the line shapes. Here a rate equation model, which includes two spatial dimensions, is developed, and reasonable agreement is obtained between experimental and theoretical data.