A purely ionic interpretation of the tilting-mode instabilities in La 2− x A x CuO 4 (A Sr, Ba) is shown to be not self-consistent: the dominant factor influencing the doping dependence of the interlayer mismatch is the large change in the CuO bond length. But such a large dependence of the bond length on valence leads to a strong electron-phonon coupling, contradicting the assumption that covalent effects were negligible. This coupling is closely related to the vHS-JT effect. This new insight clarifies the role of the tilt-mode instabilities. The main JT coupling is not to these modes, but to the in-plane OO bond-stretching modes which split the vHS degeneracy. However, as these modes soften, they couple to the lower-lying tilt modes, so that the ultimate instability has a finite tilt component. This in turn simplifies the description of the JT instabilities. The tilt modes, while strongly coupled to the electrons, are quadratic in the tilt angle. On the other hand, the bond-stretch modes have a large, linear coupling to electrons, with clear polaronic effects. This is connected with the fact that, near a vHS, valence fluctuations are slow and relatively long lived, coupling to local phonon modes. A striking result of this is that there will be a large polaronic band narrowing near the vHS, whether or not the vHS is near the Fermi level. This vHS localized band narrowing provides a natural explanation for the common occurrence of extended vHS's.