Our programme involves the study of Am stars of differing temperatures and luminosities as well as of the Am stars deviating from the positions of the classical ones in the photometric diagrams. We have found for certain stars a significant disagreement between the so-called ‘abundance indices’ and the abundances determined at high dispersion. Often giants or spectroscopic binaries, or stars with a detectable rotation, are involved. However, there are no consistant relationships between these different peculiarities and the observed disagreements. We shall give some examples of stars studied by us. Are these ‘abundance indices’ really what they are supposed to be in all cases? In which cases are they not and why?