  In the edge-triangle model with edge density close to 1/2 and triangle
density below 1/8 we prove that the unique entropy-maximizing graphon is
symmetric bipodal. We also prove that,for any edge density $e$ less than $e_0 =
(3-\sqrt{3})/6 \approx 0.2113$ and triangle density slightly less than $e^3$,
the entropy-maximizing graphon is not symmetric bipodal.
