The saturated absorption technique is an elegant method widely used in atomic and molecular physics for high-resolution spectroscopy, laser frequency standards and metrology purposes. We have recently discovered that a saturated absorption scheme with a dual-frequency laser can lead to a significant sign reversal of the usual Doppler-free dip, yielding a deep enhanced-absorption spike. In this paper, we report detailed experimental investigations of this phenomenon, together with a full in-depth theoretical description. It is shown that several physical effects can support or oppose the formation of the high-contrast central spike in the absorption profile. The physical conditions for which all these effects act constructively and result in very bright Doppler-free resonances are revealed. Apart from their theoretical interest, results obtained in this manuscript are of great interest for laser spectroscopy and laser frequency stabilization purposes, with applications in laser cooling, matter-wave sensors, atomic clocks or quantum optics.