  Let $\f: X \ra Z$ be a proper surjective map from a smooth complex manifold
$X$ onto a normal variety $Z$. If $\f$ has connected fibers and $-K_X$ is
$\f$-ample then $\f$ is called a good contraction. In the present paper we
study good contractions, fibers of which have dimension less or equal than two:
after describing possible two dimensional isolated fibers we discuss their
scheme theoretic structure and the geometry of $\f:X\ra Z$ nearby such a fiber.
If $dimX=4$ and $\f$ is birational with an isolated 2 dimensional fiber then we
obtain a complete description of $\f$. We provide also a description of a 4
dimensional conic fibration with an isolated fiber which is either a plane or a
quadric. We construct pertinent examples.
