  We study Alexeev and Brion's moduli scheme $M_\Gamma$ of affine spherical
varieties with weight monoid $\Gamma$ under the assumption that $\Gamma$ is
free. We describe the tangent space to $M_\Gamma$ at its `most degenerate
point' in terms of the combinatorial invariants of spherical varieties and
deduce that the irreducible components of $M_\Gamma$, equipped with their
reduced induced scheme structure, are affine spaces.
