This paper investigates the compression of infrared images with three codecs: JPEG2000, JPEG-XT and HEVC. Results are evaluated in terms of SNR, Mean Relative Squared Error (MRSE) and the HDR-VDP2 quality metric. JPEG2000 and HEVC perform fairy similar and better than JPEG-XT. JPEG2000 performs best for bits-per-pixel rates below 1.4 bpp, while HEVC obtains best performance in the range 1.4 to 6.5 bpp. The compression performance is also evaluated based on maximum errors. These results also show that HEVC can achieve a precision of 1°C with an average of 1.3 bpp.