Typically, encoding the signals of Ambisonic microphone arrays is done by either (i) a least-squares approach based on the measured or modelled directional array responses, or (ii) the theoretical frequency-dependent order-weights of the spherical harmonics decomposed microphone signals. In either case, the high frequencies are not mapped with the correct magnitude. They are under- represented when using least-squares encoding above the spatial aliasing frequency, or over-emphasized when the encoding is based on the reciprocal order-weights. To enforce a correct high-frequency magnitude, this paper proposes an additional magnitude constraint for the least-squares solution. Moreover, the addition of quadratic constraints permits further improvement: By constraining all components of the covariance matrix, not just its trace, the encoding achieves a superior representation of diffuse fields, in addition to the timbral improvement.