Sea-Bird 911(plus) conductivity-temperature-depth (CTD) data are scrutinized for the determination of the buoyancy frequency N in deep (Mediterranean Sea) waters, where N is very small (O(f)), f is the inertial frequency. Precise knowledge of such low stability values is imperative for the understanding of inertio-gravity wave propagation in the ocean. In this paper, truly homogeneous layers that are neutral in stability, N = 0, are not just detected by computing N(z) over a particular pressure window Δp, as such N includes errors due to mismatches of all sensors, but foremost by inspecting individual profiles of directly measured quantities, like temperature T and its variance change with respect to the adiabatic lapse rate Γ. Depending on the size of Δp, neutral stability can be computed in the deep layer of homogeneous water to within an error of ~0.8f (using Δp = 100 dbar) and ~0.4f (Δp = 600 dbar). The latter error is about half due to the imprecise measurement of Γ due to poor resolution of the T sensor. The former error is largely due to the (in)accuracy of individual sensors of the CTD and/or their imperfect measurement of dynamical heterogeneity in T and salinity S due to mismatch in sensor response time. This heterogeneity in T and S can be more abundant in stratified waters, where it seems more difficult to detect the appropriate value of nonzero but small N. This is fully attributable to the problem of variable length scales of stability motions that are supported by the stratification, while modifying it.