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The projections of small ice crystals (with maximum dimension <50 μm) appear quasi-circular when imaged by probes on aircraft flying through cloud. Therefore, idealized models constructed to calculate their single-scattering properties have included quasi-spherical models such as Chebyshev particles, Gaussian random spheres, and droxtals. Recently, an ice analogue grown from sodium fluorosilicate solution on a glass substrate, with several columns emanating from a common center of mass, was shown to be quasi-circular when imaged by state-of-the-art cloud probes. In this study, a new idealized model, called the budding Bucky ball (3B) that resembles the shape of the small ice analogue is developed. The corresponding single-scattering properties (scattering phase function <i>P</i><sub>11</sub> and asymmetry parameter <i>g</i>) are computed by a ray-tracing code. Compared with previously used models, 3B scatters less light in the forward and more light in the lateral and backward directions. The Chebyshev particles and Gaussian random spheres show smooth and featureless <i>P</i><sub>11</sub>, whereas droxtals and 3Bs, which have a faceted structure, show several peaks in <i>P</i><sub>11</sub> associated with angles of minimum deviation. Overall, the difference in the forward (lateral; backward) scattering between models are up to 22% (994%; 132%), 20% (510%; 101%), and 16% (146%; 156%) for small ice crystals with respective area ratios of 0.85, 0.77, and 0.69. The <i>g</i> for different models varies by up to 25%, 23%, and 19% for particles with area ratios of 0.85, 0.77, and 0.69, respectively. Because the single-scattering properties of small ice crystals depend both on the choice of the idealized model and the area ratios used to characterize the small ice crystals, higher resolution observations of small ice crystals or direct observations of their single-scattering properties are required.