The graphical nature of prominent modelling notations, such as the standards UML and SysML, enables them to tap into the cognitive benefits of diagrams. However, these notations hardly exploit the cognitive potential of diagrams and are only partially graphical with invariants and operations being expressed textually. The Visual Contract Language (VCL) aims at improving visual modelling; it tries to (a) maximise diagrammatic cognitive effectiveness, (b) increase visual expressivity, and (c) level of rigour and formality. It is an alternative to UML that does largely pictorially what is traditionally done textually. The paper presents the results of a controlled experiment carried out four times in different academic settings and involving 43 participants, which compares VCL against UML and OCL and whose goal is to provide insight on benefits and limitations of visual modelling. The paper's hypotheses are evaluated using a crossover design with the following tasks: (i) modelling of state space, invariants and operations, (ii) comprehension of modelled problem, (iii) detection of model defects and (iv) comprehension of a given model. Although visual approaches have been used and advocated for decades, this is the first empirical investigation looking into the effects of graphical expression of invariants and operations on modelling and model usage tasks. Results suggest VCL benefits in defect detection, model comprehension, and modelling of operations, providing some empirical evidence on the benefits of graphical software design.