  Consider real bivariate polynomials f and g, respectively having 3 and m
monomial terms. We prove that for all m>=3, there are systems of the form (f,g)
having exactly 2m-1 roots in the positive quadrant. Even examples with m=4
having 7 positive roots were unknown before this paper, so we detail an
explicit example of this form. We also present an O(n^{11}) upper bound for the
number of diffeotopy types of the real zero set of an n-variate polynomial with
n+4 monomial terms.
