Corrugated feed horns offer excellent beam symmetry, main beam efficiency, and crosspolar response over wide bandwidths, but can be challenging to fabricate. An easier-tomanufacture smooth-walled feed is explored that approximates these properties over a finite bandwidth. The design, optimization and measurement of a monotonically-profiled, smoothwalled scalar feedhorn with a diffraction-limited -7° FWHM is presented. The feed was demonstrated to have low cross polarization (<-30 dB) across the frequency range 33-45 GHz (30% fractional bandwidth). A return loss better than -28 dB was measured across the band.