Correlations are established between structural, thermal, and flexibility data of crystalline, locally flexible polymers giving rise to mesomorphic phases, which can be usefully organized in two classes. While in all mesophases the chain conformation is substantially disordered, in class 1 chain packing is characterized by orientation-dependent attractive interactions, so that the transition enthalpy DeltaH(ML) from the mesophase to the liquid is of the same order of magnitude as the crystal --> mesophase transition enthalpy DeltaH(CM). Conversely, in mesophases belonging to class 2 and in the corresponding melts nonbonded intermolecular interactions and conformational statistics are roughly similar, so that the M --> L transition involves very little enthalpy (DeltaH(ML) similar to 0). Consistent with the absence of specific interchain interactions, class 2 mesophases exhibit hexagonal packing and density lower than the corresponding crystalline phase. Polymers giving rise to this type of mesophase are characterized by numerous, regularly spaced side groups, often chemically different from the chain skeleton. The key factor stabilizing class 2 mesophases over the melt appears to be a higher entropy of the side groups, making mesogenic groups unnecessary. Optimization of the intrachain arrangement in class 2 mesophases usually requires a local contraction along the chain axis direction with respect to the extension found in the crystal and the confinement of individual chains within tubes that have a diameter D substantially larger than the average diameter D-C in the crystal. With a simple statistical model based on continuum elasticity (the self-compacting chain), applicable to flexible polymers, we show that, consistent with the available experimental data, the persistence length P is proportional to D-2. As a consequence, the aspect ratio P/D, which is normally assumed to control mesophase stability, is proportional to D. According to our approach, we thus may estimate by simple diffraction measurements of D the persistence length and the class 2 mesophase stability of flexible polymers. In the case of systems which experimentally give rise to class 2 mesophases, relatively large values of P are found despite the relatively low T,