Narrow-band laser performance of alcohol solutions of pyrromethene 567 (PM567) and rhodamine 6G (RH6G) dye was investigated using a home-made GIG- configured dye laser, excited by the second-harmonic radiation (at 532 nm) of a pulsed Nd:YAG laser. Higher laser efficiency was observed with PM567 dye ($\sim 23%$ peak) in comparison to the commonly used RH6G dye (16.5%), in spite of much lower fluorescence quantum efficiency of the PM567 (0.83) vis-à-vis RH6G (0.98) dye solutions in ethanol. First principle-based electronic structure calculations were performed on PM567 dye in the ground ($S_{0}$) and excited states ($S_{1}$) using density functional theory to elucidate the structure and photophysical properties of the dye.