Thick origami expands on the traditional paper-thin origami and engineers methods to flat fold rigid thick plates with hinges. Numerous techniques have been investigated to retain the essential qualities of zero-thickness origami, including tapered panels (Tomohiro in Origami 5(5):253–264, 2011), offset panels, shifted hinges, doubled hinges, rolling contacts, membranes, and strained joints (Lang et al. in Appl Mech Rev 70(1):010805, 2018). However, less study has been done on the rigid plates in thick origami structures compared to the hinges. This paper seeks to broaden the scope of this field by investigating the geometric properties of plates. The paper introduces a novel concept termed “not-so-thick” origami, which aims to reduce the flat-fold thickness of origami structures through interlocking rigid plates. Two case studies focusing on bi-fold and Z-fold configurations demonstrate the effectiveness of this approach in achieving significant reductions in folded thickness compared to conventional thick origami methods. These innovations open up new possibilities for designing and utilizing origami-inspired structures with enhanced compactness and functional versatility.