The acoustic response of phospholipid-coated microbubble ultrasound contrast agents (UCA) is dramatically affected by their stabilizing shell. The interfacial shell elasticity increases the resonance frequency, the shell viscosity increases damping, and the nonlinear shell viscoelasticity increases the generation of harmonic echoes that are routinely used in contrast-enhanced ultrasound imaging. To date, the surface area-dependent interfacial properties of the phospholipid coating have never been measured due to the extremely short time scales of the MHz frequencies at which the microscopic bubbles are driven. Here, we present high-precision acoustic measurements of the dilatational nonlinear viscoelastic shell properties of phospholipid-coated microbubbles. These highly accurate measurements are now accessible for the first time by tuning the surface dilatation, that is, the lipid packing density, of well-controlled monodisperse bubble suspensions through the ambient pressure. Upon compression, the shell elasticity of bubbles coated with DPPC and DPPE-PEG5000 was found to increase up to an elasticity of 0.6 N m-1 after which the monolayer collapses and the elasticity vanishes. During bubble expansion, the elasticity drops monotonically in two stages, first to an elasticity of 0.35 N m-1, and then more rapidly to zero. Integration of the elasticity vs. surface area curves showed that, indeed, a phospholipid-coated microbubble is in a tensionless state upon compression, and that it reaches the interfacial tension of the surrounding medium upon expansion. The measurements presented in this work reveal the detailed features of the nonlinear dilatational shell behavior of micron-sized lipid-coated bubbles.