The Rh-Te and Ir-Te binary systems for 50-78 atom % Te show remarkable differences in their phase and structural features at temperatures below 1100 °C. Extended Hückel calculations are employed to investigate the influence of various orbital interactions on these differences. In general, a strong interrelationship among valence electron count, orbital characteristics at and near the Fermi levels, and relative strengths of M-Te, Te-Te, and M-M orbital interactions control the occurrence and structures of various MxTe2 compounds (0.75 ≤ x ≤ 2). Stronger Ir-Te than Rh-Te orbital interactions lead to the different low-temperature structures of IrTe2 (CdI2-type) and RhTe2 (pyrite-type), but then short and intermediate-range Te-Te interactions lead to the pyrite-type structure for the defect phases M1-uTe2. At temperatures above 600 °C, RhTe2 (pyrite-type) is unstable relative to disproportionate to the "stuffed" CdI2-type Rh1+xTe2 and the defect pyrite-type Rh1-uTe2. The Rh-rich phases, Rh1+xTe2, show ordered vacancies in alternating layers of octahedral holes and can be formulated as (Rh3)x(Rh)1-2xTe2 (x ≤ 1/2) and (Rh3)1-x(Rh)4x-2Te2 (x ≥ 1/2) to emphasize the occurrence of linear Rh3 units in their structures. The pattern of vacancies in these structures follows the preference of Rh4n+3 oligomers over Rh4n+1 chains. Charge-iterative calculations of Rh atomic orbital energies in Rh1+xTe2 (x = 0.0, 0.5, 1.0) were carried out to analyze the electronic properties of Rh throughout the series. As x increases, Rh-Te orbital interactions become less attractive and the concentration of Rh-Rh repulsive interactions grows. Both effects control the maximum value of x (observed to be 0.84) for this series and influence the pattern of occupied octahedral holes in the close-packed tellurium matrix.