  Given $m\in \mathbb{N},$ a numerical semigroup with multiplicity $m$ is
called packed numerical semigroup if its minimal generating set is included in
$\{m,m+1,\ldots, 2m-1\}.$ In this work, packed numerical semigroups are used to
built the set of numerical semigroups with fixed multiplicity and embedding
dimension, and to create a partition in this set. Moreover, Wilf's conjecture
is checked in the tree associated to some packed numerical semigroups.
