  We study the geometric and combinatorial effect of smoothing an intersection
point in a collection of arcs or curves on a surface. We prove that all taut
arcs with fixed endpoints and all taut 1-manifolds with at least two
non-disjoint components on an orientable surface with negative Euler
characteristic admit a taut smoothing, and also that all taut arcs with free
endpoints admit a smoothing that is either taut or becomes taut after removing
at most one intersection. We deduce that for every Riemannian metric on a
surface, the shortest properly immersed arcs with at least $k$
self-intersections have exactly $k$ self-intersections when the endpoints of
the arc are fixed, and at most $k+1$ self-intersections otherwise, and that the
arc length spectrum is "coarsely ordered" by self-intersection number. Along
the way, we obtain partial analogous results in the case of curves.
