We present a study of weak near-IR absorption lines in 44 low luminosity YSOs. Using a spectral resolution of similar to 1000 most Class II sources show CO overtone absorption bands of varying strength in the K window, whether they have optical counterparts or not. Class I sources tend to show featureless 2 mu m continua even though a S/N > 100 was achieved. High resolution (R=17000) echelle spectra were also obtained for a sub-sample of YSOs. Most show an unresolved (CO)-C-12(2-0) bandhead, which when combined with inferred CO excitation temperatures and optical depths dearly points to a photospheric rather than a disk origin for the bands. They also show that embedded Class IIs are not rapidly rotating. We find an excellent correlation between increasing near-IR colour excess and decreasing band strength and interpret this in a straightforward way as due to veiling of the stellar photosphere by circumstellar dust emission at 1000-1200 K, probably from a disk. A veiling correction was applied and intrinsic indices obtained for many YSOs. The results provide confirmation that Class II sources are equivalent to T Tauri stars.