We calculate the electrostatic noise spectrum that should be measured by an antenna immersed in a plasma with a ''flat-top'' electron velocity distribution function, for frequencies of the order of the plasma frequency fp. We find that the main part of the spectrum is nearly the same as the thermal noise in a Maxwellian plasma with the same density and equivalent temperature, while the peak near fp depends on the high-energy tail of the distribution. We consider both wire dipole and double-sphere antennae, and deduce some practical consequences for plasma wave measurements in the Earth magnetosheath. ¿ American Geophysical Union 1989