  In a previous work we have introduced and studied the notion of embedded
$\mathbf{Q}$-resolution, which essentially consists in allowing the final
ambient space to contain abelian quotient singularities. Here we explicitly
compute an embedded $\mathbf{Q}$-resolution of a Yomdin-L\^e surface
singularity $(V,0)$ in terms of a (global) embedded $\mathbf{Q}$-resolution of
their tangent cone by means of just weighted blow-ups at points. The
generalized A'Campo's formula in this setting is applied so as to compute the
characteristic polynomial. As a consequence, an exceptional divisor in the
resolution of $(V,0)$, apart from the first one which might be special,
contributes to its complex monodromy if and only if so does the corresponding
divisor in the tangent cone. Thus the resolution obtained is optimal in the
sense that the weights can be chosen so that every exceptional divisor in the
$\mathbf{Q}$-resolution of $(V,0)$, except perhaps the first one, contributes
to its monodromy.
