When thinking about giftedness in digital age, we have to pay our attention to counselling to perfectionist students as well, for it is well documented that the perfectionism can enhance or hinder giftedness. Psychological school-counselling experiences with gifted students are discussed within the current literature on perfectionism and perfectionism in gifted students. The author's approach to counselling is mainly based on cognitive paradigm. The paper primarily focuses on understanding of perfectionism as a multidimensional construct and as a personal trait; the emphasis is on specific perfectionistic cognitive patterns, emotional reactions, behaviour and social relations of perfectionistic gifted secondary school students. Although numerous studies exist regarding perfectionism of gifted students there is little attention paid to school-counselling practise. In the paper it is discussed how perfectionism contributes to some psychological issues of gifted secondary school students and describes some of the consequences for their mental health. Finally it is shown why it is important for school counsellor to understand and differentiate between students with healthy strivings to achieve high standards and those with forced persistence aiming to reach unrealistically high goals, feeling dissatisfaction and showing inadequacy unless achieving.