We evaluate the relative importance of three-dimensional (3D) effects and ice crystal shape of spatially heterogeneous cirrus on the remote-sensing of optical thickness and effective crystal radius. In current ice cloud retrievals, the single scattering properties of ice crystals have to be assumed a-priori. Likewise, the effects of spatial cloud heterogeneity are ignored in current techniques. Both simplifications introduce errors in the retrievals. Our study is based on 3D and independent pixel approximation (IPA) radiative transfer calculations. As model input we used a cloud case that was generated from data collected during the NASA Tropical Composition, Cloud, and Climate Coupling (TC4) experiment. First, we calculated spectral upwelling radiance fields from the input cloud as they would be sensed by sensors from space or aircraft. We then retrieved the cirrus optical thickness and crystal effective radius that would be obtained in standard satellite techniques under the IPA assumption. The ratios between retrieved and the original fields are used as a metric for cloud heterogeneity effects on retrievals. Second, we used different single scattering properties (crystal shapes) in the retrievals than those used in the radiance calculations. In order to isolate ice crystal habit effects, the net horizontal photon transport was disabled in this part of the study. Here, the ratios between retrieved and original values of optical thickness and effective radius serve as metric for ice crystal habit effects. When comparing the two metrics, we found that locally, both can be of the same magnitude (up to 50% over- and underestimation), with different dependencies on cirrus optical thickness, effective radius, and optical thickness variability. On domain average, shape effects bias the retrievals more strongly than 3D effects.