Let H be a 3-uniform hypergraph. The multicolor Ramsey number rk(H) is the smallest integer n such that every coloring of (3[n]) with k colors has a monochromatic copy of H. Let
L be the loose 3-uniform path with 3 edges and M
denote the messy 3-uniform path with 3 edges; that is, let L={abc,cde,efg} and M={abc,bcd,def}. In this note we
prove rk(L)<1.55k and rk(M)<1.6k for k
sufficiently large. The former result improves on the bound rk(L)<1.975k+7k, which was recently established by {\L}uczak and Polcyn.Comment: 18 pages, 3 figure