  Let K be a knot in S^3 of genus g and let n>0. We show that if rk HFK(K,g) <
2^{n+1} (where HFK denotes knot Floer homology), in particular if K is an
alternating knot such that the leading coefficient a_g of its Alexander
polynomial satisfies |a_g| <2^{n+1}, then K has at most n pairwise disjoint
non-isotopic genus g Seifert surfaces. For n=1 this implies that K has a unique
minimal genus Seifert surface up to isotopy.
