  Let $K$ be a tunnel number one knot in $M$, where $M$ is either $S^3$, or a
connected sum of $S^2\times S^1$ with any lens space. (In particular this
includes $M = S^2\times S^1$.) We prove that if a Dehn surgery on $K$ yields a
non-trivial lens space, then $K$ is a doubly primitive knot in $M$. For $M =
S^3$ this resolves the tunnel number one Berge Conjecture. For $M = S^2\times
S^1$ this resolves a conjecture of Greene and Baker-Buck-Lecuona for tunnel
number one knots.
