The complex nature of mental well-being is reflected in the great diversity of variables thought to represent aspects of mental flourishing. Discovering the underlying structure of mental well-being is important for a full understanding of this complex construct. Using data from 3 countries (the United States, Japan, and Iran), we performed multi-dimensional scaling to analyze the representation of 9 hedonic and eudaimonic well-being variables in a 2-dimensional psychological space. The analyses revealed 2 interpretable underlying dimensions across cultures and gender groups. The first dimension-eudaimonic well-being versus hedonic well-being-is well-known to well-being researchers. The second dimension-existential relatedness versus Epicurean independence-has not been recognized before. Existential relatedness is the characteristic of being meaningfully interconnected with things other than oneself, and is mainly based on the variables positive relations with others, personal growth, purpose in life, and life satisfaction. Epicurean independence is the characteristic of being relatively free of painful experiences and not feeling the need to have ones' views accepted by anyone but oneself. Epicurean independence is mainly based on the variables autonomy and absence of negative affect. We explain these dimensions in detail and discuss the implications for well-being research and policy.