Some cognitive dimensions are internationally considered by psychologists to describe and to assess creativity. For example, (Guilford, P. (1976). Creatividad y Educacion. Buenos Aires. Ed. Paidos) and (Torrance, E. P. (1977). Discovery and nurturance of giftedness in the culturally different. Reston, VA: Council on Exceptional Children) suggested fluency, flexibility, originality and elaboration are the main cognitive processes used to define and assess creativity. However, data from several empirical studies did not confirm a factor structure in accordance with such cognitive functions, despite of the wide use of TTCT (Torrance Tests of Creative Thinking) in different countries. In this paper, we present new data collected in Spain and Portugal with TTCT. According to our data, those cognitive functions supposedly present on a subject's performance are not so strong as to explain the variance in scores. Elaboration factors assume some variance explanation, but the main factors are identified with the products in each subtest, suggesting the importance of format, content and demand on TTCT specific tasks. Consequently, we suggest some reflections to amplify the debate concerning the definition of creativity and its evaluation in psychology.