Traditionally, corrugated conical horn antennas have been the main choice for use in astronomical receivers in the range of millimeter and submillimeter waves. They present low cross-polar level and high coupling efficiency into the fundamental Gaussian mode. However, this type of antenna is difficult to manufacture, inevitably increasing its price and extending the production process. In this work, we present two kinds of feed horn antennas, aimed for use in the ALMA Band-6 frequency range (211-275 GHz), which can be fabricated in a much simpler way with conventional machining tools. Specifically, we present the design and performance comparison of smooth-walled spline-profile horns in two geometries, diagonal and conical. Optimization of the designs has been made by means of an algorithm that allowed us to obtain models whose electrical and mechanical characteristics make them competitive when compared with corrugated horns. Our simulations have shown a good cross-polar performance with levels below −20dB and gaussicity above 96%. These properties make this type of horns an option at the time of choosing a feed system for cutting-edge astronomical applications.