AlGaInAs/InP waveguide-coupled deformed hexagonal resonator microlasers with enhanced mode quality (Q)-factors are demonstrated for realizing single-transverse-mode operation. A circular hole is introduced to the center of the hexagonal resonators with rounded corners to enhance the mode Q-factors and suppress high-order transverse modes simultaneously. Single-mode lasing with side-mode suppression ratios up to 40 dB is obtained for the 10-μm-sidelength hexagonal microlasers with a center hole. All the lasing spectra demonstrate pure single-transverse-mode properties within the whole tuning range of injection current, and mode hopping with one, two, and three longitudinal-mode intervals is observed due to the mode Q-factor modification by the center holes. To further reduce the device size and threshold current, the deformed hexagonal resonator microlasers with the flat sides replaced by circular arcs are analyzed and demonstrated experimentally. The Q-factors of the fundamental transverse modes can be enhanced by two orders of magnitude due to the convergence effect of the circular sides by optimizing the deformation amplitude, while the single-transverse-mode property is still maintained. A threshold current of 2.4 mA is realized for a circular-side hexagonal microlaser with the side length of 8.5 μm and the deformation amplitude of 0.55 μm.