Downregulation of MHC class I molecules is a strategy developed by some viruses to escape cellular immune responses. Myxoma virus (MV), a poxvirus causing rabbit myxomatosis, encodes MV-LAP that is known to increase MHC-I endocytosis and degradation through a C(4)HC(3) motif critical for an E3 ubiquitin ligase activity. Here, we performed a functional mapping of MV-LAP and showed that not only the C(4)HC(3) motif is necessary for a marked downregulation of MHC-I but also a conserved region in the C-terminal part of the protein. We also showed that the putative transmembrane domains are responsible for a specific subcellular localization of the protein: they retain MV-LAP in the ER in transfected cells and in the endolysosomal compartments in infected cells. We observed that a specific MV infection context is necessary for a fully efficient downregulation of MHC-I. Our data suggest that the functionality of viral LAP factors, inherited by herpes- and poxviruses from mammalian cells, is more complex than anticipated.