  We prove some cases of the Fontaine-Mazur conjecture for even Galois
representations. In particular, we prove, under mild hypotheses, that there are
no irreducible two-dimensional ordinary even Galois representations of
$\Gal(\Qbar/\Q)$ with distinct Hodge-Tate weights. If $K/\Q$ is an imaginary
quadratic field, we also prove (again, under certain hypotheses) that
$\Gal(\Qbar/K)$ does not admit irreducible two-dimensional ordinary Galois
representations of non-parallel weight. Finally, we prove that any weakly
compatible family of two dimensional irreducible Galois representations of
$\Gal(\Qbar/\Q)$ is, up to twist, either modular or finite.
