Improving drug delivery efficiency to solid tumor sites is a central challenge in anti-cancer therapeutic research. Our previous experimental study (Guo et al., Nat. Commun. 2018, 9, 130) showed that soft, elastic liposomes had increased uptake and accumulation in cancer cells and tumors in vitro and in vivo respectively, relative to rigid particles. As a first step towards understanding how liposomes’ molecular structure and composition modulates their elasticity, we performed all-atom and coarse-grained classical molecular dynamics (MD) simulations of lipid bilayers formed by mixing a long-tailed, unsaturated phospholipid with a short-tailed saturated lipid with the same head group. The former type of phospholipids considered were 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) and 1,2-dipalmitoleoyl-sn-glycero-3-phosphocholine (termed here DPMPC). The shorter saturated lipids examined were 1,2-diheptanoyl-sn-glycero-3-phosphocholine (DHPC), 1,2-didecanoyl-sn-glycero-3-phosphocholine (DDPC), 1,2-dilauroyl-sn-glycero-3-phosphocholine (DLPC), and 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC). Several lipid concentrations and surface tensions were considered. Our results show that DOPC or DPMPC systems having 25-35 mol% of the shortest lipids DHPC or DDPC are the least rigid, having area compressibility moduli KA that are ~10% smaller than the values observed in pure DOPC or DPMPC bilayers. These results agree with experimental measurements of the stretching modulus and lysis tension in liposomes with the same compositions. These systems also have lower areas per lipid, form more uneven x-y interfaces with water, the tails of both primary and secondary lipids are more disordered, and the terminal methyl groups in the tails of the long lipids DOPC or DPMPC wriggle more in the vertical direction, compared to pure DOPC or DPMPC bilayers or their mixtures with the longer saturated lipids DLPC or DMPC. These observations confirm our hypothesis that adding increasing concentrations of the short unsaturated lipids DHPC or DDPC to DOPC or DPMPC bilayers, alters lipid packing and thus make the resulting liposomes more elastic and less rigid. No formation of lipid nanodomains was noted in our simulations, and no clear trends were observed in the lateral diffusivities of the lipids as concentration, type of secondary lipid and surface tension were varied.