  A word $u$ is a scattered factor of $w$ if $u$ can be obtained from $w$ by
deleting some of its letters. That is, there exist the (potentially empty)
words $u_1,u_2,..., u_n$, and $v_0,v_1,..,v_n$ such that $u = u_1u_2...u_n$ and
$w = v_0u_1v_1u_2v_2...u_nv_n$. We consider the set of length-$k$ scattered
factors of a given word w, called here $k$-spectrum and denoted
$\ScatFact_k(w)$. We prove a series of properties of the sets $\ScatFact_k(w)$
for binary strictly balanced and, respectively, $c$-balanced words $w$, i.e.,
words over a two-letter alphabet where the number of occurrences of each letter
is the same, or, respectively, one letter has $c$-more occurrences than the
other. In particular, we consider the question which cardinalities $n=
|\ScatFact_k(w)|$ are obtainable, for a positive integer $k$, when $w$ is
either a strictly balanced binary word of length $2k$, or a $c$-balanced binary
word of length $2k-c$. We also consider the problem of reconstructing words
from their $k$-spectra.
