  The global deformation theory of residually reducible Galois representations
with fixed auxiliary conditions is studied. We show that
$\bar{\rho}:\operatorname{Gal}(\bar{\mathbb{Q}}/\mathbb{Q})\rightarrow
\operatorname{GL}_2(\bar{\mathbb{F}}_p)$ lifts to a Hida line for which the
weights range over a congruence class modulo-$p^2$. The advantage of the purely
Galois theoretic approach is that it allows us to construct $p$-adic families
of Galois representations lifting the actual representation $\bar{\rho}$, and
not just the semisimplification.
