We give a geometric proof of the following result of Juhasz. \emph{Let ag​
be the leading coefficient of the Alexander polynomial of an alternating knot
K. If ∣ag​∣<4 then K has a unique minimal genus Seifert surface.} In
doing so, we are able to generalise the result, replacing `minimal genus' with
`incompressible' and `alternating' with `homogeneous'. We also examine the
implications of our proof for alternating links in general.Comment: 37 pages, 28 figures; v2 Main results generalised from alternating
links to homogeneous links. Title change