The ratio of ground-state densities Ro ≡ N (13CO) / N (C18O) has been used to infer physical and chemical conditions in giant molecular clouds (Wannier et al. 1976) and dark clouds (Mahoney et al. 1976; Langer et al. 1979). In dark clouds Ro is found to vary from values near the terrestrial ratio [13C] [16O] / [12C] [18O] ∼ 5 at positions of high extinction to values ∼20 at positions of low extinction. In this paper we present high-resolution J = 1 → 0 spectra of CO, 13CO, and C18O at positions of high extinction in TMC-2, L134, and L134N. The C18O lines have non-Gaussian wings and are ∼ half as wide as the 13CO lines. We find that RO must vary across the line, from a minimum of R0 ∼ 4 at the peak of the C18O line to a maximum of RO ∼ 10 in the wings, unless the 13CO line has peak opacity ∼5. The variation of RO with position and with velocity is consistent with models of clouds which have a dense core with low velocity-dispersion and low fractionation, and a rarefied envelope with high velocity-dispersion and high fractionation.