Doppler-free spectra of the D-1 line of potassium have been studied fo
r different intensities of the pump and probe beams and at different o
rientations of magnetic field. Particular attention was paid to the cr
ossover resonances that combine transitions from different sublevels o
f the ground state. At small intensities, all details of the observed
spectra are in good agreement with theory. At moderate and large inten
sities, the above-mentioned crossovers dominate; however, they do not
differ much in the cases of pi and sigma(+/-) selection rules. The fir
st observation is in accordance with qualitative analysis and the resu
lts of a simple three-level model, while the second one is not. It is
explained in terms of quasi-dark states, which are formed when the Rab
i frequency becomes greater than the Larmor frequency and which withdr
aw atoms from cycling transitions.