In this paper, we propose a 2-layer lossless coding method for high dynamic range (HDR) images based on range compression and adaptive inverse tone-mapping. Recently, HDR images, which have a wider range of luminance than conventional low dynamic range (LDR) ones, have been frequently used in various fields. Since commonly used devices cannot yet display HDR images, 2-layer coding methods that decode not only HDR images but also their LDR versions have been proposed. We have previously proposed a state-of-the-art 2-layer lossless coding method for HDR images that unfortunately has huge HDR file size. Hence, we introduce two ideas to reduce the HDR file size to less than that of the previous method. The proposed method achieves high compression ratio and experiments show that it outperforms the previous method and other conventional methods.