Generative processes and generative design approaches are topics of continuing interest and debate within the realms of architectural design and related fields. While they are often held up as giving designers the opportunity (the freedom) to explore far greater numbers of options/alternatives than would otherwise be possible, questions also arise regarding the limitations of such approaches on the design spaces explored, in comparison with more conventional, human-centric design processes. This article addresses the controversy with a specific focus on parametric-associative modelling and genetic programming methods of generative design. These represent two established contenders within the pool of procedural design approaches gaining increasingly wide acceptance in architectural computational research, education and practice. The two methods are compared and contrasted to highlight important differences in freedoms and limitations they afford, with respect to each other and to ‘manual’ design. We conclude that these methods may be combined with an appropriate balance of automation and human intervention to obtain ‘optimal’ design freedom, and we suggest steps towards finding that balance.