  We provide a method for factoring all bounded ratios of the form $$\det
A(I_1|I_1')\det A(I_2|I_2')/\det A(J_1|J_1')\det A(J_2|J_2')$$ where $A$ is a
totally positive matrix, into a product of more elementary ratios each of which
is bounded by 1, thus giving a new proof of Skandera's result. The approach we
use generalizes the one employed by Fallat et al. in their work on principal
minors. We also obtain a new necessary condition for a ratio to be bounded for
the case of non-principal minors.
