Cochleates are self-assembled cylindrical condensates that consist of large rolled-up lipid bilayer sheets and represent a novel platform for oral and systemic delivery of therapeutically active medicinal agents. With few preceding investigations, the physical basis of cochleate formation has remained largely unexplored. We address the structure and stability of cochleates in a combined experimental/theoretical approach. Employing different electron microscopy methods, we provide evidence for cochleates consisting of phosphatidylserine and calcium to be hollow tubelike structures with a well-defined constant lamellar repeat distance and statistically varying inner and outer radii. To rationalize the relation between inner and outer radii, we propose a theoretical model. Based on the minimization of a phenomenological free energy expression containing a bending, adhesion, and frustration contribution, we predict the optimal tube dimensions of a cochleate and estimate ratios of material constants for cochleates consisting of phosphatidylserines with varied hydrocarbon chain structures. Knowing and understanding these ratios will ultimately benefit the successful formulation of cochleates for drug delivery applications.