  We prove that if $e$ is a join-irreducible element of a semimodular lattice
$L$ of finite length and $h<e$ in $L$ such that $e$ does not cover $h$, then
$e$ can be "lowered" to a covering of $h$ by taking a length-preserving
semimodular extension $K$ of $L$ but not changing the rest of join-irreducible
elements. With the help of our "lowering construction", we prove a general
theorem on length-preserving semimodular extensions of semimodular lattices,
which implies some earlier results proved by G. Gr\"atzer and E. W. Kiss
(1986), M. Wild (1993), and G. Cz\'edli and E. T. Schmidt (2010) on extensions
to geometric lattices, and even an unpublished result of E. T. Schmidt on
higher dimensional rectangular lattices. Our method offers shorter proofs of
these results than the original ones. To obtain the main tool used in the
paper, we extend the bijective correspondence between finite semimodular
lattices and Faigle geometries to an analogous correspondence between
semimodular lattices of finite lengths and a larger class of geometries.
