We present a study of the nebular phase spectra of a sample of Type II-Plateau supernovae with identified progenitors or restrictive limits. The evolution of line fluxes, shapes and velocities is compared within the sample, and interpreted by the use of a spectral synthesis code. The small diversity within the data set can be explained by strong mixing occurring during the explosion, and by recognizing that most lines have significant contributions from primordial metals in the H envelope, which dominates the total ejecta mass in these types of objects. In particular, when using the [O i] 6300, 6364 Å doublet for estimating the core mass of the star, care has to be taken to account for emission from primordial O in the envelope. Finally, a correlation between the Hα line width and the mass of 56Ni is presented, suggesting that higher energy explosions are associated with higher 56Ni production.