The study of volitional personality change has received increasing attention in recent years, suggesting that individuals want to change for the better particularly on those socially desirable characteristics that they lack. However, individuals do not want to change for the better on all (even socially desirable) traits alike. In a meta-analytic summary of evidence on the Big Five, we demonstrate that individuals’ trait levels are only negatively related to their change goals for Neuroticism, Extraversion, and Conscientiousness, but not for Agreeableness and Openness to Experience. In three studies, two of them preregistered, we replicated these meta-analytic findings using the HEXACO model, showing negative relations between trait levels and change goals for all dimensions, except Honesty-Humility and Openness to Experience. Strikingly, however, these trait-specific differences in correlations of trait levels and change goals disappeared once providing individuals with personality feedback before assessing their change goals, suggesting that individuals may generally want to change for the better once having sufficient self-knowledge. Nonetheless, the mechanisms driving this desire differ between traits: Whereas the perceived social desirability of individuals’ trait levels accounted for change goals on most HEXACO dimensions, it did not account for change goals on Honesty-Humility and Openness to Experience. By implication, a desire to have socially desirable characteristics that one lacks can explain change goals for some traits, but not for those traits underlying individual differences in values. As an aside, the studies offer vital information on personality development of the HEXACO dimensions over time, spanning 10 and 3.5 years, respectively.