  We give an general estimate for the non-microstates free entropy dimension
$\delta ^{*}(X_{1},..., X_{n})$. If $X_{1},..., X_{n}$ generate a diffuse von
Neumann algebra, we prove that $\delta ^{*}(X_{1},..., X_{n})\geq 1$. In the
case that $X_{1},..., X_{n}$ are $q$-semicircular variables as introduced by
Bozejko and Speicher and $q^{2}n<1$, we show that $\delta ^{*}(X_{1},...,
X_{n})>1$. We also show that for $|q|<\sqrt{2}-1$, the von Neumann algebras
generated by a finite family of $q$-Gaussian random variables satisfy a
condition of Ozawa and are therefore solid: the relative commutant of any
diffuse subalgebra must be hyperfinite. In particular, when these algebras are
factors, they are prime and do not have property $\Gamma $.
