We study links using the crossing-ball technique of W.
Menasco and define special positions for spanning surfaces in link
complements. We show that if a given spanning surface is in special
position, then the boundary of a neighborhood of the surface is in standard
position. Thus we can work on a closed surface in the link complement
instead of working on a surface with boundary. We also mension that if
a link admits an almost alternating diagram, then we can cut its spanning
surface to be in special position.