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For a second-order system settling time to a given band is -ln(tolerance)/(zeta x omega_n), so the 2% settling time is about 4/(zeta omega_n). Overshoot depends only on damping ratio: 0.7 gives about 4.6%, and 0.5 gives 16%.
Second-order response
ts = -ln(tolerance) / (zeta x wn); overshoot = 100 x exp(-pi zeta / sqrt(1 - zeta^2))
It gives about 4-5% overshoot with the fastest settling for a given natural frequency, and corresponds to a maximally flat frequency response.
Increase omega_n (higher loop gain or stiffer mechanics) rather than reducing damping, which trades settling time for overshoot.