We study some properties of the Venereau polynomials b_m=y+x^m(xz+y(yu+z^2)),
a sequence of proposed counterexamples to the Abhyankar-Sathaye embedding
conjecture and the Dolgachev-Weisfeiler conjecture. It is well known that these
are hyperplanes and residual coordinates, and for m at least 3, they are
C[x]-coordinates. For m=1,2, it is only known that they are 1-stable
C[x]-coordinates. We show that b_2 is in fact a C[x]-coordinate. We introduce
the notion of Venereau-type polynomials, and show that these are all
hyperplanes, and residual coordinates. We show that some of these Venereau-type
polynomials are in fact C[x]-coordinates; the rest remain potential
counterexamples to the embedding and other conjectures. For those that we show
to be coordinates, we also show that any automorphism with one of them as a
component is stably tame. The remainder are stably tame, 1-stable
C[x]-coordinates.Comment: 15 pages; to appear in J. Pure and Applied Algebr
