Individual-level trait diversity has been identified as an essential component of trait diversity (TD), influencing community assembly and structure. Traditionally, one employs trait diversity indices to measure facets of individual-level trait diversity (divergence, richness and evenness). However, the application of species-level trait diversity indices to individual-level traits data and their implications have not been adequately studied. Thus, we examined the possible challenges of using four commonly used multi-trait TD indices: Rao's quadratic entropy (Rao), functional dispersion (FDis), functional evenness (FEve) and functional richness (FRic); two indices primarily developed to measure individual-level trait diversity: trait evenness distribution (TED-for evenness) and trait onion peeling (TOP-for richnness); and a modified version of TED (TEDM-for evenness). Additionally, we considered an index that integrates both evenness and richness by generalizing ordinary Hill indices for traits (coined HIT). We measured individual-level trait diversity with these indices using simulated traits data and experimental data from a growth experiment with cyanobacteria. Comparing the observed trends from the indices with the expected trends, we observed that only the trait divergence indices (FDis and Rao) produced the expected trends in the simulation scenarios and experimental data. TED and TEDM are not robust against the number of individuals used, and FEve is not sensitive to some changes in the location of individuals in the trait space. Also, TOP proved to be a discontinuous function dependent on the number of individuals, and FRic did not produce the anticipated trend when changes in the trait space did not affect the edges of the trait space. HIT did produce the anticipated changes, but it was only reliable when many individuals were sampled. In summary, applying these individual-level trait diversity indices to quantify anything except trait divergence may lead to misinterpretation of the original situation of trait distribution in the trait space if their specific properties are not adequately considered.