It is a common expectation that analytical rotations of factors and components aiming for a simple structure allow dimensions of intercorrelated, manifest variables to be identified with a high degree of certainty. A recently presented counter-model, the rotation to complex structure supported by a large number of investigations fundamentally calls this assumption into question. This paper examines the claimed advantage of a rotation to complex structure with the aid of artificially generated data structures whose components were predetermined. For similarity comparisons, it has been possible to show that only a rotation to complex structure provides interpretable and realistic solutions. (C) 2015 Elsevier Ltd. All rights reserved.