Let Fn := K1 + nK2 be a fan of order 2n + 1. For 1 ≤ s < t, we consider the weakened Gallai-Ramsey number grst(Fn), defined to be the least p ∈ ℕ such that every Gallai t-coloring of Kp contains a subgraph isomorphic to Fn whose edges use at most s colors. Our main results include the evaluations gr2t(F2) = t + 3, gr23(F3) = 9, and gr2n − 1t(Fn) = 2n + 1.