Inelastic neutron scattering, supported by IR and Raman spectroscopy, has been used to observe a decreasing Pd-H bond strength in a series of four low-valent palladium-hydrogen complexes in the solid-state hydrides: K-2[Pd(II)H-4], Li-2[Pd(0)H-2], Na-2[Pd(0)H-2], NaBa[Pd(0)H-3], and Ba-2[Pd(0)H-4]. Further, self-consistent linear muffin-tin orbital calculations of the electronic structures describe the palladium-hydrido complexes in a sd(n) hybridization with a decreasing Pd-H bond order as an increasing number of antibonding orbitals must be utilized. A strong support to the bonding from the cations via easily polarizable H- is, however, necessary to explain the stability of the systems. The effect of the large polarizability of hydrogen can in this respect be compared with the more conventional "back-bonding" to ligand orbitals for stabilizing a formal low-valent oxidation state by distributing electron density away from the central atom.