  We study stable reduction of curves in the case where a tamely ramified base
extension is sufficient. If X is a smooth curve defined over the fraction field
of a strictly henselian discrete valuation ring, there is a criterion, due to
T. Saito, that describes precisely, in terms of the geometry of the minimal
model with strict normal crossings of X, when a tamely ramified extension
suffices in order for X to obtain stable reduction. For such curves we
construct an explicit extension that realizes the stable reduction, and we
furthermore show that this extension is minimal. We also obtain purely
geometric proof of Saito's criterion, avoiding the use of vanishing cycles.
