  Let $X$ be a proper smooth algebraic variety over a field $k$ of
characteristic zero and let $D$ be a divisor with simple normal crossings. Let
$M$ be a vector bundle over $X-D$ equipped with a flat connection with possible
irregular singularities along $D$. We define a cleanliness condition which
roughly says that the singularities of the connection are controlled by the
singularities at the generic points of $D$. When this condition is satisfied,
we compute explicitly the associated log-characteristic cycle, and relate it to
the so-called refined irregularities. As a corollary of a log-variant of
Kashiwara-Dubson formula, we obtain the Euler characteristic of the de Rham
cohomology of the vector bundle, under a mild technical hypothesis on $M$.
