  Coupled cluster theory is an attractive tool to solve the quantum many-body
problem because its singles and doubles (CCSD) approximation is computationally
affordable and yields about 90% of the correlation energy. Capturing the
remaining 10%, e.g. via including triples, is numerically expensive. Here we
assume that short-range three-body correlations dominate and - following Lepage
[How to renormalize the Schr\"odinger equation, arXiv:nucl-th/9706029] - that
their effects can be included within CCSD by renormalizing the three-body
contact interaction. We renormalize this contact in $^{16}$O and obtain
accurate CCSD results for $^{24}$O, $^{20-34}$Ne, $^{40,48}$Ca, $^{78}$Ni,
$^{90}$Zr, and $^{100}$Sn.
