  This paper is a companion paper to [G4], where sharp estimates are proven for
Fourier transforms of compactly supported functions built out of
two-dimensional real-analytic functions. The theorems of [G4] are stated in a
rather general form. In this paper, we expand on the results of [G4] and show
that there is a class of "well-behaved" functions that contains a number of
relevant examples for which such estimates can be explicitly described in terms
of the Newton polygon of the function. We will further see that for a subclass
of these functions, one can prove noticeably more precise estimates, again in
an explicitly describable way.
