  Let f: Y -> CP^2 be a birational morphism of non-singular (rational)
surfaces. We give an effective (necessary and sufficient) criterion for
algebraicity of the surfaces resulting from contraction of the union of the
strict transform of a line on CP^2 and all but one of the exceptional divisors
of f. As a by-product we construct normal non-algebraic Moishezon surfaces with
the `simplest possible' singularities, which in particular completes the answer
to a remark of Grauert. Our criterion involves `global variants' of `key
polynomials' introduced by MacLane. The geometric formulation of the criterion
yields a correspondence between normal algebraic compactifications of C^2 with
one irreducible curve at infinity and algebraic curves in C^2 with one place at
infinity.
