The basis set convergence of nuclear spin-spin coupling constants (SSCC) calculated at the coupled cluster singles and doubles (CCSD) level has been investigated for ten difficult molecules. Eight of the molecules contain fluorine atoms and nine contain double or triple bonds. Results obtained using the ccJ-pVXZ, X=D,T,Q,5, hierarchy of basis sets of Benedikt et al. [J. Chem. Phys. 129, 064111 (2008)], converge rather slowly towards the basis set limit, but fast convergence can be obtained by adding diffuse functions, in particular for couplings across several bonds. The pcJ-n basis sets of Jensen [J. Chem. Theory Comput. 2, 1360 (2006)] exhibit large contraction errors for one-bond couplings, but in their uncontracted form they perform better than the ccJ-pVXZ basis sets. For multi-bond couplings, however, diffuse functions should be used, and when including these the two hierarchies show similar performance. The ccJ-pVXZ basis sets with diffuse functions included (aug-ccJ-pVXZ) show consistent performance across all types of SSCCs, with the triple zeta (X=T) basis set yielding sufficiently good results for most purposes.