The author studies quasi-projective uniserial modules over a valuation domain

$R$ and, in particular, quasi-projective ideals of

$R$. The quasi-projectivity of a uniserial

$R$-module

$U$ is characterized in terms of lifting of endomorphisms of factors of

$U$ and this characterization is used to describe quasi-projective ideals of

$R$ in terms of the completeness of certain localizations of factor rings of

$R$. In the case of archimedean ideals this description becomes more explicit and it is shown that, if the maximal ideal

$P$ of

$R$ is infinitely generated, a non-principal archimedean ideal

$I$ is quasi-projective if and only if

$R/K$ is complete in the

$R/K$-topology for each archimedean ideal

$K\ncong P$ (and, in this case, all archimedean ideals of

$R$ are quasi-projective).