Retrievals of ice cloud properties using infrared measurements at 3.7, 6.7, 7.3, 8.5, 10.8, and 12.0 µm can provide consistent results regardless of solar illumination, but are limited to cloud optical thicknesses τ < ~6. This paper investigates the variations in radiances at these wavelengths over a deep convective cloud system for their potential to extend retrievals of τ and ice particle size De to optically thick clouds. Measurements from an imager, an interferometer, the Cloud Physics Lidar (CPL), and the Cloud Radar System (CRS) aboard the NASA ER-2 aircraft during the NASA TC4 (Tropical Composition, Cloud and Climate Coupling) experiment flight during 5 August 2007, are used to examine the retrieval potential of infrared radiances over optically thick ice clouds. Simulations based on coincident in situ measurements and combined cloud τ from CRS and CPL measurements are comparable to the observations. They reveal that brightness temperatures at these bands and their differences (BTD) are sensitive to τ up to ~20 and that for ice clouds having τ > 20, the 3.7-10.8µm and 3.7-6.7µm BTDs are the most sensitive to De. Satellite imagery appears to be consistent with these results suggesting that τ and De could be retrieved for greater optical thicknesses than previously assumed. But, because of sensitivity of the BTDs to uncertainties in the atmospheric profiles of temperature, humidity, and ice water content, and sensor noise, exploiting the small BTD signals in retrieval algorithms will be very challenging.