First we report benchmark high-level calculations for the barrier heights of five degenerate and nearly degenerate rearrangements (CH3. + CH4 or C2H6, C2H5. + CH4 or C2H6, and n-C3H7. + n-C3H8) involving hydrogen transfer between hydrocarbon fragments. Then the performance of 11 existing and 5 new semiempirical methods based on the neglect of diatomic differential overlap (NDDO) and the intermediate neglect of differential overlap (INDO) is evaluated by comparing their predictions to those of the more accurate levels. All methods are additionally tested against a representative test suite of reactive barrier heights and a representative test suite of bond energies. Two new NDDO methods, each with one Gaussian function parametrized for reactions involving the transfer of hydrogen atoms between carbon centers, were developed to provide both accurate barrier heights and transition-state geometries. The results show that the energetic barriers for the transfer of hydrogen between carbon centers calculated by one of the existing NDDO levels, in particular, Austin model 1 (AMI), and by these two new methods, denoted AM1-CHC-SRP and PM3-CHC-SRP, agree well with the more accurate results and in particular have mean unsigned errors of only 1.9, 1.4, and 0.7 kcal/mol, respectively, and give reasonable transition-state geometries. Thirteen other NDDO and INDO methods (in particular, PM3, PM3tm, PM3-AHR, PM3-NHR, PM3-3H2, PM5, MNDO, MNDO/d, MNDOC, SAM1, MSINDO, PDDG/PM3, and PDDG/MNDO) that are tested have mean unsigned errors of 3.5-34 kcal/mol or qualitatively incorrect transition-state geometries for such transfers. Another interesting finding of this study is that hybrid density functional theory methods do not agree with high-level explicitly correlated methods for the trend in barrier height when methyl is changed successively to ethyl and n-propyl in the degenerate rearrangements. This indicates that they make different predictions about trends in the intrinsic barrier height parameter of Marcus theory and that the intrinsic barrier heights are very sensitive to approximations in the treatment of exchange and correlation.