  We use Heegaard Floer homology to give obstructions to unknotting a knot with
a single crossing change. These restrictions are particularly useful in the
case where the knot in question is alternating. As an example, we use them to
classify all knots with crossing number less than or equal to nine and
unknotting number equal to one. We also classify alternating knots with ten
crossings and unknotting number equal to one.
