  We study the Directed Polymer model subject to a particular form of disorder,
$\eta(x,t)=\eta_X(x) \eta_T(t)$, recently proposed in biological applications.
We find that two new universality classes arise, depending on the the lattice
geometry. Using an intermediate model linking the two different orientations
continuously, we find that there is a phase transition separating two distinct
scaling phases. For both phases we get a reasonable understanding of the nature
and values of the exponents, corroborated with numerical results.
