We show that the leading coefficient of the Kazhdan--Lusztig polynomial
$P_{x,w}(q)$ known as $\mu(x,w)$ is always either 0 or 1 when $w$ is a Deodhar element of a
finite Weyl group. The Deodhar elements have previously been characterized using pattern
avoidance by Billey--Warrington (2001) and Billey--Jones (2007). In type $A$, these
elements are precisely the 321-hexagon avoiding permutations. Using Deodhar's (1990)
algorithm, we provide some combinatorial criteria to determine when $\mu(x,w) = 1$ for such
permutations $w$.