Across the tree of life, distinct designs of cellular membranes have evolved that are both stable and flexible. In bacteria and eukaryotes this trade-off is accomplished by single-headed lipids that self-assemble into flexible bilayer membranes. By contrast, archaea in many cases possess both bilayer and double-headed, monolayer spanning bolalipids. This composition is believed to enable extremophile archaea to survive harsh environments. Here, through the creation of a minimal computational model for bolalipid membranes, we discover trade-offs when forming membranes using lipids of a single type. Similar to living archaea, we can tune the stiffness of bolalipid molecules. We find that membranes made out of flexible bolalipid molecules resemble bilayer membranes as they can adopt U-shaped conformations to enable higher curvatures. Conversely, stiffer bolalipid molecules, like those found in archaea at higher temperatures, preferentially take on a straight conformation to self-assemble into liquid membranes that are stable, stiff, prone to pore formation, and which tear during membrane reshaping. Strikingly, however, our analysis reveals that it is possible to achieve the best of both worlds – membranes that are fluid, stable at high temperatures and flexible enough to be reshaped without leaking – through the inclusion of a small fraction of bilayer lipids into a bolalipid membrane. Taken together, our study compares the different membrane designs across the tree of life and indicates how combining lipids can be used to resolve trade-offs when generating membranes for (bio)technological applications.