A new optical characterization of the behavior of single ultrasound contrast bubbles is presented. The method consists of insonifying individual bubbles several times successively sweeping the applied frequency, and to record movies of the bubble response up to 25 million frames/s with an ultrahigh speed camera operated in a segmented mode. The method, termed microbubble spectroscopy, enables to reconstruct a resonance curve in a single run. The data is analyzed through a linearized model for coated bubbles. The results confirm the significant influence of the shell on the bubble dynamics: shell elasticity increases the resonance frequency by about 50%, and shell viscosity is responsible for about 70% of the total damping. The obtained value for shell elasticity is in quantative agreement with previously reported values. The shell viscosity increases significantly with the radius, revealing a new nonlinear behavior of the phospholipid coating.