In feedhorn design, the power coupling to the fundamental free-space LG(00) mode, or Gaussicity, is a good proxy for high performance, particularly the sidelobe and cross-polar levels and the near-field behavior. Gaussicity can be maximized by ensuring that the first few horn modes reach the aperture with the appropriate phase and amplitude relationship. We present two feedhorn designs for which the Gaussicity was maximized in order to achieve high performance. The first is a 94 GHz corrugated horn with a tanh-linear profile, manufactured by electroforming, which achieves a Gaussicity of 99.92% at band center and sidelobes at the -60 dB level. The second is a 340 GHz smooth-walled spline horn which achieves a Gaussicity of >99.2% over a 10% bandwidth, sidelobes below -30 dB and excellent near-field behavior. This design has been successfully fabricated in E-plane split block suitable for low volume manufacture, for example for imaging arrays.