The applicability of the discrete dipole approximation (DDA) is examined to estimate backscattering signatures of ice crystals randomly oriented in horizontal plane (2-D) and oriented in three-dimensional space (3-D) for various sizes and aspect ratios at the frequency of 95 GHz (3.16 mm). Previous studies have shown that accurate estimation of the backscattering properties seem to be problematic for particles with sharp edges and fixed in one orientation with respect to the incident radar wave. Contrary, the errors in the backscattering calculations for 2-D and 3-D orientations are drastically reduced and turn out to be less than 10% for both radar reflectivity factor Ze and linear depolarization ratio (LDR). Exception is the LDR for hexagonal plates with 2-D orientation, where it is not possible to achieve a converging solution. Then the size-averaged Ze and LDR for various aspect ratios are estimated as a function of effective radius reff, for the first time, with a confidence of accuracy. The differences in Ze for different shapes or orientations are within 2 dB (40%), and thus the size is a control parameter for reff 100 ¿m, Ze and LDR show strong dependence on shape as well as size. Due to the fact that the local minimum and maximum of Ze and LDR occur at different reff depending on the shape, nonsphericity plays a major role for reff > 100 ¿m, where the maximum differences between Ze for the different shapes are 8 dB and those for LDR are 14 dB. For reff > 1000 ¿m, the maximum differences between the LDRs for the different shapes are 5 dB, while the effect of orientations becomes comparable, although such larger particles are rare in cirrus clouds.