Bullying can be differentiated from other types of peer aggression by four key characteristics: frequency, intensity, power imbalance, and goal‐directedness. Existing instruments, however, usually assess the presence of these characteristics implicitly. Can self‐report instruments be refined using additional questions that assess each characteristic? We examined (a) what proportion of children classified as victims by the commonly used Revised Olweus’ bully/victim questionnaire (BVQ) also experienced the characteristics of bullying, and (b) the extent to which the presence of the characteristics was associated with emotional (affect, school, and classroom well‐being), relational (friendship, defending), and social status (popularity, rejection) adjustment correlates among victims. Using data from 1,738 students (Mage = 10.6; grades 5–8), including 138 victims according to the BVQ, the results showed that 43.1% of the children who were classified as victims by BVQ experienced all the four characteristics of bullying. Frequency ratings of victimization did not capture experiences that involved a power imbalance. Victims who reported all four key characteristics had greater emotional, relational, and social status problems than victims who did not report all characteristics. Thus, researchers who focus on victimization for diagnostic and prevention purposes can enrich self‐report measurements of bullying victimization by adding questions that assess the characteristics explicitly.