  We describe a new algebraic technique, utilising transfer matrices, for
enumerating self-avoiding lattice trails on the square lattice. We have
enumerated trails to 31 steps, and find increased evidence that trails are in
the self-avoiding walk universality class. Assuming that trails behave like $A
\lambda ^n n^{11 \over 32}$, we find $\lambda = 2.72062 \pm 0.000006$ and $A =
1.272 \pm 0.002$.
