  We study irreducible mod p representations, valued in general reductive
groups, of the Galois group of a number field. When the number field is totally
real, we show that odd representations satisfying local ramification hypotheses
and a certain multiplicity-free condition on the adjoint representation admit
geometric lifts. For general number fields, we show without any oddness or
multiplicity condition that the representation admits a p-adic lift if it does
everywhere locally.
