We study Wilf's conjecture for numerical semigroups S such that the second least generator a2 of S satisfies a2 > c(S)+μ(S) 3, where c(S) is the conductor and μ(S) the multiplicity of S. In particular, we show that for these semigroups Wilf's conjecture holds when the multiplicity is bounded by a quadratic function of the embedding dimension.
