<p>The method of moments is widely used for analyzing and designing of various types of antennas with wire grids. Some design recommendations are known, but they are not suitable for the initial wire grids, to which the recently proposed optimal current grid approximation is applicable to create sparse antennas with a lower mass. In this work, new recommendations are proposed for the design of initial wire-grid (WG) structures for conical horn antennas with various equivalent excitation models. The recommendations form new design guidelines for the wire-grid conical horn antennas with different equivalent excitation models. The guidelines are verified by applying them to conical horn antennas operating in different frequency bands. The obtained antenna characteristics for the WG-structures are in good agreement with those obtained experimentally and numerically using other methods. In addition, this work presents the results of applying the modified optimal current grid approximation to the original structures designed according to the proposed recommendations for sparse structures. In special cases, these structures can be used to replace the solid metal structure, as well as the original WG-structures while maintaining the required characteristics. The results of this work allow us to quickly and accurately design original WG-structures for conical horn antennas with acceptable characteristics for efficient creation of sparse antennas.</p>