The novel notion of locked (or 'stuck') polygons opens the possibility of constructing three-dimensional linear polymers that are effectively knotted due to the occurrence of differential local rigidity along the chain. Here, we show that effective knotting is theoretically possible even in short chains. Our results imply the existence of a finite range of polymer lengths over which an oligopeptide can adopt a locked-polygon conformation. We discuss briefly a number of settings where these conformer topologies may be experimentally observable.