One group of hypotheses suggests archaeal and/or bacterial ancestry of eukaryotes, while the second group suggests that the ancestor of eukaryotes was different. Especially, the followers of the first group of hypotheses should ask the following: is the replacement of archaeal lipids by bacterial (or vice versa) possible? Do the phylogenies support the origin of one domain from another (or the others)? Can we consider the nutritional mode to resolve the problems of cell origin(s)? Is there any evidence that the ancestor of eukaryotes was intron-free? Would the symbiosis of α-proteobacterial ancestors of mitochondria be successful in an asexual host? Is there evidence that the last universal common ancestor (LUCA) or the last eukaryotic common ancestor was bounded by one membrane only? With respect to the current knowledge about cells and their molecular components, the answer to most of these questions is: No! A model for the origins of domains is briefly presented which cannot be assigned as false through the current scientific data, and is rather consistent with the assumption that eukaryotes are direct descendants of neither archaea nor bacteria. It is proposed that the domain Bacteria arose the first, and that the last common ancestor of Archaea and Eukarya was a pre-cell or a progenote similar to LUCA. The pre-karyote (the host entity for α-proteobacterial ancestors of mitochondria) was probably bounded by two membranes, possessed spliceosomal introns and spliceosomes, was sexual, and α-proteobacterial ancestors of mitochondria were most likely parasites of the pre-karyote periplasm (intermembrane space).