In engineering design, constraints can stimulate creativity but are also often cited as obstacles to innovation. So do constraints hinder or foster creativity? Despite a number of studies, the reason why constraints can have a positive or a negative impact on creativity is still unknown. In this paper, we will propose, theoretically and empirically, that the link between creativity and constraints is not determined by the type of constraints, but by the type of 'design model' used. Using C-K theory, a well-documented, general, and formalized theory of design, we first prove that the dual impact of constraints on creativity is predictable. Then we use C-K operators to distinguish two different design models: rule-based design and innovative design. We show that the first model organizes a negative link between constraints and creativity while the second model enables a positive effect. We illustrate these mechanisms through the analysis of several product developments based on both secondary and primary sources.