The paper presents an undertaking to develop most compact high dynamic range image compression format and shows that chromatic color coordinate system plays a central role in such development. Important design considerations, such as conditions and criterions of data accuracy, efficiency and characteristics of color space, are addressed along the way. An additional trade-off between data precision and data size is discussed, and new feature of parameterized precision is introduced. Detailed comparison of Bef, Luv, Yxy chromatic coordinates is performed and special case of color space singularities is analyzed. LinLogBef imaging format implementation is presented and compared against OpenEXR and Radiance HDR formats by compression ratio, relative error and dynamic range characteristics. Other benefits provided by LinLogBef are further discussed, such as the format's convenience for image editing operations.