In vivo hepatic 1H lineshapes modeled by the complex Voigt function are desirable to reduce systematic error and obtain accurate fits. However, the optimization procedure becomes challenging when the peak resonances overlap and the proportion of Gaussian to Lorentzian dampings is a priori unknown. In this context, nonlinear least-squares algorithms generally invoked in Magnetic Resonance Spectroscopy quantification are highly sensitive to the starting values and parameter bounds. To alleviate this sensitivity, multiple random starting values and parameter bounds settings are used to generate candidate solutions. The "best fit" fulfilling requirements on the cost function and damping factor final values is then selected among them. Monte Carlo studies and an in vivo hepatic 1H signal quantification demonstrated the relevance of the proposed strategy.