In „Ellipsoids of maximal volume in convex bodies“ Keith Ball proved a general bound on the volume of k-dimensional ellipsoids in n-dimensional convex bodies in relation to their John ellipsoid. A stronger bound is known in the symmetric case. Our goal was to connect these results by establishing a bound depending on the John asymmetry s_0. We could prove a tight bound for all k and all asymmetry values s_0 not in (1,1+2/n), and characterize the equality cases.