  A locally conformally K\"ahler (LCK) manifold $M$ is one which is covered by
a K\"ahler manifold $\tilde M$ with the deck transform group acting conformally
on $\tilde M$. If $M$ admits a holomorphic flow, acting on $\tilde M$
conformally, it is called a Vaisman manifold. Neither the class of LCK
manifolds nor that of Vaisman manifolds is stable under small deformations. We
define a new class of LCK-manifolds, called LCK manifolds with potential, which
is closed under small deformations. All Vaisman manifolds are LCK with
potential. We show that an LCK-manifold with potential admits a covering which
can be compactified to a Stein variety by adding one point. This is used to
show that any LCK manifold M with potential, $\dim M > 2$, can be embedded to a
Hopf manifold, thus improving on similar results for Vaisman. manifolds.
