Two levels of creativity can be identified whether we look at the concept from the product, the person or the process point of view. The one is radical and revolutionary, the other adaptive and confirmatory. Are there organizational structures and practices that support lower level creativity but hamper higher level, or vice versa? Some research results on organizational climate and structure variables are presented that indicate differing influences on higher and lower level creativity. It is argued that the issue of innovation in organizations harbours a couple of basic dilemmas, the management of which requires understanding and taking into consideration the psychology of creativity.