  We address the problem of &#64257;nding nice labellings for event structures
of degree 3. We develop a minimum theory by which we prove that the labelling
number of an event structure of degree 3 is bounded by a linear function of the
height. The main theorem we present in this paper states that event structures
of degree 3 whose causality order is a tree have a nice labelling with 3
colors. Finally, we exemplify how to use this theorem to construct upper bounds
for the labelling number of other event structures of degree 3.
