The use of pairwise dispersion corrections together with dispersion-correcting potentials (DCPs) offers a computationally low-cost approach to improving the performance of a density-functional theory based method with respect to the prediction of important chemical properties. In this work, we develop DCPs for the C, H, N, and O atoms for use with the BLYP generalized gradient approximation functional coupled with "D3" pairwise dispersion corrections and 6-31+G(2d,2p) basis sets. The combined approach, referred to as BLYP-D3-DCP, offers generally improved performance over both unadorned BLYP and BLYP with D3 corrections with respect to the prediction of noncovalent binding energies (BEs) and covalent bond dissociation enthalpies (BDEs). Predicted barrier heights for a set of pericyclic and Diels-Alder reactions are improved in some instances, as are organic bond separation reaction energies and radical stabilization energies. It is also shown that the BLYP-D3-DCP approach outperforms B3LYP-D3 in the prediction of many chemical properties, in particular noncovalent BEs and BDEs, suggesting that the addition of D3 and DCP corrections, which have negligible computational cost, to simple density functionals like BLYP may elevate their performance to that of more complex functionals such as B3LYP.