  By the Lefschetz embedding theorem, a principally polarized $g$-dimensional
abelian variety is embedded into projective space by the linear system of $4^g$
half-characteristic theta functions. Suppose we {\em edit} this linear system
by dropping all the theta functions vanishing at the origin to order greater
than parity requires. We prove that for Jacobians the edited $4\Theta$ linear
system still defines an embedding into projective space. Moreover, we prove
that the projective models of Jacobians arising from the elementary
construction of Jacobians recently given by the author are (after passage to
linear hulls) copies of the edited $4\Theta$ model. Thus, for all compact
Riemann surfaces, we tie together algebraic and analytic Jacobians in a new
way.
