  We explicitly bound T-singularities on normal projective surfaces $W$ with
one singularity, and $K_W$ ample. This bound depends only on $K_W^2$, and it is
optimal when $W$ is not rational. We classify and realize surfaces attaining
the bound for each Kodaira dimension of the minimal resolution of $W$. This
answers effectiveness of bounds (see [Alexeev94], [Alexeev-Mori04], [Lee99])
for those surfaces.
