Membrane lipid species are not identically distributed in the inner and outer leaflet of biological membranes. This metastable asymmetric distribution of lipids is called `lipid asymmetry', and it is an important feature of many biological membranes. Investigation of various aspects of lipid asymmetry has been limited by a lack of robust methods to prepare stable artificial asymmetric vesicles. We recently developed a method in which methyl-beta-cyclodextrin (MβCD)-induced lipid exchange is used to prepare model membrane vesicles with lipid asymmetry and which, like eukaryotic plasma membranes, have an outer leaflet rich in sphingomyelin (SM) and have an inner leaflet rich in ordinary glycerophospholipids, such as phosphatidylcholine, phosphatidylethanolamine, and phosphatidylserine. The range of this method has been extended to generate asymmetric vesicles containing SM in the outer leaflet and phospholipids with different acyl chain and headgroup structures in the inner leaflet. The structure of acyl chains and headgroups was systematically varied, and how this variation affected the capability to exchange lipids as well as the ability to form stable asymmetric vesicles was studied. It was found that the MβCD-induced method efficiently exchanged all the lipids tested. Furthermore, we observed that the formation of stable asymmetry (SM outside/various lipids inside) depended upon the structure of acyl chain and headgroup of lipids. To characterize the origin of this behavior, the transverse diffusion (flip-flop) rate of lipids in vesicles with various acyl chain and headgroup structures was compared. It was found that there is a correlation between stable asymmetry and transverse diffusion, with transverse diffusion being slower in vesicles containing lipids from which stable asymmetric vesicles could be prepared. These studies show that asymmetric vesicles can be prepared using a wide, but not universal, range of acyl chains and headgroup structures. The presence of lipids that can undergo fast transverse diffusion prevents stable lipid asymmetry. These properties may constrain the species of lipids in natural membranes in which stable asymmetry is an important structural feature.