The connectivity-based hierarchy (CBH) protocol for computing accurate reaction enthalpies developed by Sengupta and Raghavachari 1 is tested for fast ab initio methods (PBEh-3c, HF-3c, and HF/STO-3G), tight-binding DFT methods (GFN-xTB and DFTB), and NDDO-based semi-empirical methods (AM1, PM6, PM6-DH+, PM7, and OM2) using the same set of 25 reactions as in the original study. As observed by Sengupta and Raghavachari 1 , the CBH-1 correction scheme, which reflects the change in bonding, provides only a modest improvement in accuracy and for many of the semi-empirical methods the error actually increases. For the CBH-2 scheme, which reflects the change in the immediate chemical environment of all the heavy atoms, the MUE relative to G4 of PBEh-3c is 1.9 kcal/mol which is very similar to the 1. While the accuracy is lower for the minimal basis set and semiempirical methods are lower than for PBEh-3c, they are significantly more computationally efficient with HF-3c and HF/STO-3G being roughly 10-50 times faster and the semiempirical methods being roughly 1000 times faster, depending on system size. It is worth noting that GFN-xTB is roughly 10 times faster than the other semiempirical methods, which can lead to significant time savings when dealing with thousands of molecules. However, significant changes in bonding and/or unusual bonding still presents are challenge to these faster methods as evidenced by the presence of outliers.