This paper had two related aims; firstly, to establish the appropriateness of phenomenological research to the field of project management (PM) as an antecedent to secondly, exploring the use of ‘analytic induction’ as a method that might have utility in the analysis of qualitative data in the field of project management. Managing projects is key to the development of change in social systems and is closely associated with innovation and sustainable outcomes. However, normative project management has been criticised for its lack of utility and efficacy in practice and does not appear to wholly represent the ‘lived experience’ of practitioners. In PM literature, the ‘rethinking project management’ research initiative sought to address this, proposing that research into the management of projects must take account of the need to develop ‘theory for practice’. In support of this, PM literature has charted and proposed a move away from deterministic approaches towards non-deterministic approaches in order to better understand persistent issues in project management. Part of the problem of normative PM’s irrelevance might have been the lack of methodological rigour in PM research. This raises the question of whether and what post-positivist research approaches are more suitable for PM research? This paper considers the issues and suitability of post-positivist, non-deterministic, and constructivist/phenomenological approaches to PM research. By way of illustration, ‘analytic induction’ (AI) (a method from social science which seems an appropriately comparative field) is considered a rigorous post-positivist inductive and qualitative method that might be employed in the reworking of PM theory to produce alternative paradigms of project and PM. An example PM study that utilised AI is reflected on in this paper and found that: AI provides a level of rigour necessary to address PM’s research challenges; that care over sample homogeneity is critical to such studies; and that adaptation of the original AI method, (the inclusion of deviant samples in the final interpretations), might allow for additional rigour.