We report observed and derived timing parameters for three millisecond pulsars (MSPs) from observations collected with the Parkes 64-m telescope, Murriyang. The pulsars were found during reprocessing of archival survey data by Mickaliger et al. One of the new pulsars (PSR J1546–5925) has a spin period P = 7.8 ms and is isolated. The other two (PSR J0921–5202 with P = 9.7 ms and PSR J1146–6610 with P = 3.7 ms) are in binary systems around low-mass (⁠>0.2M⊙⁠) companions. Their respective orbital periods are 38.2 and 62.8 d. While PSR J0921–5202 has a low orbital eccentricity e = 1.3 × 10^−5, in keeping with many other Galactic MSPs, PSR J1146–6610 has a significantly larger eccentricity, e = 7.4 × 10^−3. This makes it a likely member of a group of eccentric MSP–helium white dwarf binary systems in the Galactic disc whose formation is poorly understood. Two of the pulsars are co-located with previously unidentified point sources discovered with the Fermi satellite’s Large Area Telescope, but no γ-ray pulsations have been detected, likely due to their low spin-down powers. We also show that, particularly in terms of orbital diversity, the current sample of MSPs is far from complete and is subject to a number of selection biases.Read less <