  Given a birational modification $X \to Y$ of complex projective varieties
with fiber dimension 1 and rational singularities, consider the main component
of Bridgeland's moduli space $W \to Y$ of perverse point sheaves on $X/Y$. We
give criteria for the normalization of $W$ to coincide with the transform
(flip/flop) $X^+ \to Y$ of $X \to Y$. First, this holds if the exceptional loci
of $X \to Y$ and $W \to Y$ have codimension $>1$. Second, if the ideal sheaf of
$X \times_Y X^+$ is flat over $X^+$ then there is at least a morphism $X^+ \to
W$. We illustrate the results using a number of examples, including surface
modifications and standard Francia flips.
