It is demonstrated that velocity selective optical pumping/saturation resonances of reduced absorption in a Rb vapor nanocell with thickness L= λ, 2λ, and 3λ (resonant wavelength λ = 780 nm) allow the complete elimination of crossover (CO) resonances. We observe well pronounced resonances corresponding to the Fg = 3 → Fe = 2, 3, 4 hyperfine transitions of the 85 Rb D2 line with linewidths close to the natural width. A small CO resonance located midway between Fg = 3 → Fe = 3 and Fg = 3 → Fe = 4 transitions appears only for L = 4λ. The D2 line (λ = 852 nm) in a Cs nanocell exhibits a similar behavior. From the amplitude ratio of the CO and VSOP resonances it is possible to determine the thickness of the column of alkali vapor in the range of 1 -1000 µm. The absence of CO resonances for nanocells with L ∼ λ is attractive for frequency reference application and for studying transitions between Zeeman sublevels in external magnetic fields.

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