The challenge of realigning the present path of development on a sustainable trajectory is shared among all sectors of society, including engineering. To move towards a more sustainable practice of engineering, the design process needs to be modified in order for engineers to tackle the related issues in a structured manner. Such “sustainable design processes” (SDPs) are proposed in the recent literature. By reviewing conventional as well as sustainable design processes, this paper aims to identify the major differences between the former and the latter. Critical tasks missing from SDPs proposed so far are also pointed out, according to key observations emerging from the field of sustainability science. These tasks are then combined with contributions from reviewed SDPs into a novel integrated sustainable engineering design process (ISEDP). Instead of representing conventional and sustainable engineering as a dichotomy, this paper rather places both approaches on a continuum along which the engineer or an organization can position itself. For this purpose, a procedure based on the IESDP is proposed, allowing one to assess its progress towards sustainable engineering. The method reveals different shades of sustainability along six dimensions: (1) the structure of the design process; (2) the scope of sustainability issues considered; (3) the relevance of the indicators guiding the design; (4) the accuracy of the tools used to evaluate the indicators; (5) the potential improvements expected from the alternatives assessed when compared to conventional solutions; and (6) the approach to decision making.