Single-crystal neutron diffraction, inelastic neutron scattering, and density functional calculations provide experimental and theoretical analyses of the nature of the osmium-bound, "elongated" dihydrogen ligands in [Cp*OsH4(L)][BF4] complexes (L = PPh3, AsPh3, or PCy3). The PPh3 and AsPh3 complexes clearly contain one dihydrogen ligand and two terminal hydrides; the H2 ligand is transoid to the Lewis base, and the H-H vector connecting the central two hydrogen atoms lies parallel to the Ct-Os-L plane (Ct = centroid of Cp* ring). In contrast, in the PCy3 complex the H-H vector is perpendicular to the Ct-Os-L plane. Not only the orientation of the central two hydrogen atoms but also the H-H bond length between them depends significantly on the nature of L: the H⋯H distance determined from neutron diffraction is 1.01(1) and 1.08(1) Å for L = PPh3 and AsPh3, respectively, but 1.31(3) Å for L = PCy3. Density functional calculations show that there is a delicate balance of electronic and steric influences created by the L ligand that change the molecular geometry (steric interactions between the Cp* and L groups most importantly change the Ct-Os-L angle), changing the relative energy of the Os 5d orbitals, which in turn govern the H-H distance, preferred H-H orientation, and rotational dynamics of the elongated dihydrogen ligand. The geometry of the dihydrogen ligand is further tuned by interactions with the BF4 - counterion. The rotational barrier of the bound H2 ligand in [Cp*OsH4(PPh3)]+, determined experimentally (3.1 kcal mol-1) from inelastic neutron scattering experiments, is in reasonable agreement with the B3LYP calculated H2 rotational barrier (2.5 kcal mol-1).