  This is an addendum to the paper of Braun and Fl{\o}ystad ([BF]) on the bound
for the degree of a smooth surface in $\pfour$ not of general type. Using their
construction and the regularity of curves in $\pthree$, one may lower the bound
a little more. We will prove the following:
  Theorem. Let $S$ be a smooth surface of degree $d$ in $\pfour$ not of general
type. Then either $d \leq 70$ or $S$ lies on a hypersurface in $\pfour$ of
degree 5 and $d \leq 80$. Thus $d \leq 80$. We will also indicate how to lower
the bound to 76.
