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Within the context of ambidexterity, this paper focuses on the tension between radical and incremental innovation and its main aim is to investigate whether an ambidextrous organization for innovation can be conceptualized in a more integrated way as a second‐order construct reflected by both contextual and structural approaches. Structural equation modelling is employed to analyse data from a survey of 185 firms in Austrian and Italian medium‐ and high‐tech industries. The primary contribution of the paper is that the ambidextrous organization can be meaningfully described by a higher‐order structure made up of structural and contextual solutions. This paper makes an important contribution to ambidexterity thanks to high‐order modelling of the construct of ‘ambidextrous organization’, thus unveiling interesting implications for both academics and managers.