  We determine the structure of the circular handle decompositions of the
family of free genus one knots. Namely, if k is a free genus one knot, then the
handle number h(k)= 0, 1 or 2, and, if k is not fibered (that is, if h(k)>0),
then k is almost fibered. For this, we develop practical techniques to
construct circular handle decompositions of knots with free Seifert surfaces in
the 3-sphere (and compute handle numbers of many knots), and, also, we
characterize the free genus one knots with more than one Seifert surface. These
results are obtained through analysis of spines of surfaces on handlebodies.
Also we show that there are infinite families of free genus one knots with
either h(k)=1 or h(k)=2.
