Estimation of an attenuation parameter, represented by the quality factor Q, holds paramount importance in seismic exploration. One of the main challenges in Q estimation through visco-acoustic full-waveform inversion is effectively decoupling Q from velocity. In this study, our objective is to enhance Q inversion by addressing critical aspects, including gradient preconditioning, workflow, and misfit design. By developing a new preconditioner that approximates the diagonal of the Hessian, we facilitate automatic parameter tuning across different classes, ensuring comparable magnitudes of preconditioned gradients for velocity and Q. Moreover, Our investigations confirm the efficacy of the two-stage hierarchical strategy in mitigating velocity-Q trade-offs, enabling more accurate Q estimation by first focusing on velocity reconstruction before jointly estimating velocity and Q. The analysis and numerical examples also highlight the importance of broadband data and long-offset acquisition for a reliable Q estimation. Additionally, leveraging amplitude information can improve Q estimation to some extent, but careful consideration of frequency band and noise effects is necessary. We have explored two misfit functions that capture amplitude variation with frequency in the time-frequency domain, noting their sensitivity to noise. To address this, we propose a differential strategy that can effectively mitigate the effects of low-frequency noise. This comprehensive study on enhancing Q estimation in visco-acoustic FWI offers valuable insights for multi-parameter inversion in realistic scenarios.#xD;#xD;