  We study the ribbon discs that arise from a symmetric union presentation of a
ribbon knot. A natural notion of symmetric ribbon number is introduced and
compared with the classical ribbon number. We show that the gap between these
numbers can be arbitrarily large by constructing an infinite family of ribbon
knots with ribbon number 2 and arbitrarily large symmetric ribbon number. The
proof is based on a particularly simple description of symmetric unions in
terms of certain band diagrams which leads to an upper bound for the Heegaard
genus of their branched double covers.
