We have observed 12CO J = 2-1 and J = 1-0, and 13CO J = 1-0 emission in two regions of HI Self-Absorption (HISA) in Perseus: a small, isolated HISA feature called the globule and a more extended HISA cloud called the complex. Using both Large Velocity Gradient and Monte Carlo radiative transfer codes we found that, in the globule, N(12CO) < 6.0x10^15 cm-2 which, using PDR models, implies that N(H_2) < 9.9x10^20 cm-2. In the complex we found that the H_2 column densities ranged from 1.2 - 2.2 x 10^21 cm-2. By comparing the HISA and CO observations we are able to constrain the physical conditions and atomic gas fraction (f). In the globule, 8 K < T_spin < 22 K and 0.02 < f < 0.2 depending on whether the (unknown) gas density is 10^2, 10^3, or 10^4 cm-3. In the complex, 12 K < T_spin < 24 K, 0.02 < f < 0.05, and we were also able to constrain the gas density (100 < n < 1200 cm-3). These results imply that the gas in the HISA clouds is colder and denser than that usually associated with the atomic ISM and, indeed, is similar to that seen in molecular clouds. The small atomic gas fractions also imply that there is a significant molecular component in these HISA clouds, even when little or no 12CO is detected. The level of 12CO detected and the visual extinction due to dust is consistent with the idea that these HISA clouds are undergoing a transition from the atomic to molecular phase.
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