The dispersion-core-potential corrected B3LYP-DCP method (Torres and DiLabio J. Phys. Chem. Lett. 2012, 3, 1738) is for the first time thoroughly assessed and compared with the B3LYP-NL (Hujo and Grimme J. Chem. Theory Comput. 2011, 7, 3866) and B3LYP-D3 (Grimme et al. J. Comput. Chem. 2011, 32, 1456) methods for a broad range of chemical problems that particularly shed light on intramolecular London-dispersion effects in conformers and general thermochemistry. The analysis is based on a compilation of 473 reference cases, the majority of which are taken from the GMTKN30 database (Goerigk and Grimme J. Chem. Theory Comput. 2010, 6, 107; 2011, 7, 291). The results confirm previous findings that B3LYP-DCP indeed predicts very good binding energies for noncovalently bound complexes, particularly with small basis sets. However, problems are identified for the description of intramolecular effects in some conformers and chemical reactions, for which B3LYP-DCP sometimes gives results similar or worse than uncorrected B3LYP. Surprisingly large errors for total atomization energies reveal an unwanted influence of the DCPs on the short-range electronic structure of the investigated systems. However, a recently modified carbon potential for B3LYP-DCP (DiLabio et al. Theor. Chem. Acc. 2013, 132, 1389) was additionally tested that seems to solve most of those problems and provides improved results. An overall comparison between all tested methods shows that B3LYP-NL is the most robust and accurate approach, closely followed by B3LYP-D3. This is also true when small basis sets of double-ζ quality are applied for which those methods have not been parametrized. However, binding energies of noncovalently bound complexes can be more strongly influenced by basis-set superposition-error effects than for B3LYP-DCP. Finally, it is noted that the DFT-D3 and DFT-NL schemes are readily applicable to a large range of chemical elements and they are therefore particularly recommended for more general applications.