We present details of a scheme for retrieving cirrus cloud optical thickness and effective particle size from nadir-viewing reflectance measurements. Two near-infrared wavelengths are used, one with negligible ice absorption (1.04 mu m) and one with significant ice absorption (1.55 mu m). Four ice crystal shapes are used in the scheme: ice spheres, hexagonal columns, hexagonal plates and randomized polycrystals. We highlight the sensitivity of the retrievals to the shape of the phase function, which follows from the particular ice crystal shape assumed. Five aircraft-based retrievals are presented, all cases occurring during the 1993 intensive field campaign of the European Cloud Radiation Experiment (EUCREX'93). The retrieved effective sizes are compared with the in situ measurements taken from the same cases. In these comparisons, account has to be taken of the fact that (a) in situ replicator data indicate that the presence of small (<100 mu m) ice crystals can have a significant effect on the effective crystal size, and (b) the measured crystal sizes consistently show a systematic decrease with height in all cases, the effective sizes at cloud base being typically two or three times larger than at cloud top. Taking these considerations into account, we conclude that the assumption of polycrystals gives the most consistent agreement with the in situ measurements.