We propose a procedure denoted dispersion-weighted explicitly correlated coupled-cluster [DW-CCSD(T**)-F12] which mixes CCSD(T**)-F12a and CCSD(T**)-F12b so as to correct the small errors exhibited by each of the approximations in a small basis set, allowing for a black-box method that can provide high-quality interaction energies for a variety of nonbonded interactions. Relative to CCSD(T**)-F12a and CCSD(T**)-F12b, DW-CCSD(T**)-F12 reduces the mean absolute deviation by a factor of 2 and the maximum error by a factor of 3 (formic acid dimer) and 4 (stacked adenine-thymine) for the aug-cc-pVDZ basis set.