  Catalan words are particular growth-restricted words over the set of
non-negative integers, and they represent still another combinatorial class
counted by the Catalan numbers. We study the distribution of descents on the
sets of Catalan words avoiding a pattern of length at most three: for each such
a pattern $p$ we provide a bivariate generating function where the coefficient
of $x^ny^k$ in its series expansion is the number of length $n$ Catalan words
with $k$ descents and avoiding $p$. As a byproduct, we enumerate the set of
Catalan words avoiding $p$, and we provide the popularity of descents on this
set. Some of the obtained enumerating sequences are not yet recorded in the
On-line Encyclopedia of Integer Sequences.
