  Let $I$ be an ideal whose symbolic Rees algebra is Noetherian. For $m \geq
1$, the $m$-th symbolic defect, sdefect$(I,m)$, of $I$ is defined to be the
minimal number of generators of the module $\frac{I^{(m)}}{I^m}$. We prove that
sdefect$(I,m)$ is eventually quasi-polynomial as a function in $m$. We compute
the symbolic defect explicitly for certain monomial ideals arising from graphs,
termed cover ideals. We go on to give a formula for the Waldschmidt constant,
an asymptotic invariant measuring the growth of the degrees of generators of
symbolic powers, for ideals whose symbolic Rees algebra is Noetherian.
