We investigated heteronuclear inelastic cold collisions in a mixed-species Li–Na magneto-optical trap, where the Li trap loss from collisions with Na was measured. Experimental results for the rate coefficient βNaLi for the isotopes 6Li as well as 7Li as a function of the Li-MOT laser intensity are presented. Furthermore, we discuss some unique characteristics of cold collisions of Na and Li which arise from (1) the very small spin–orbit splitting of Li, (2) the very small C6 coefficients of the Na(3 2S) + Li(2 2P) asymptotes and (3) the very small and inverted hyperfine structure of Li.