Laser-induced multianalyte atomic emissions are widely exploited for elemental analysis and sample sorting. One such scheme is UV laser-induced-fluorescence of dense plumes, or plume-LIF (PLIF) for short. For reliable analytical results, the PLIF spectra have to be properly normalized to reduce shot-to-shot variations. We theorize that the PLIF mechanism is linear and the spectra should be highly normalizable. We apply standard normalization schemes to an assortment of PLIF spectra and achieve practically complete removal of spectral fluctuations that are due to extrinsic variations. For example, the uncertainty in the brightness of the Ca I 422.7 nm line in the raw PLIF spectra of Chinese black ink can be reduced from 73% to 0.8%. Two complications can compromise normalization though. One is spectral features that arise from two-photon absorption. The other is extrinsic variations that affect spectral lineshapes.