Patients with Semantic Dementia (SD), in addition to their central semantic disorder, tend to show obsessive behaviours. Some SD cases take up jigsaw puzzles post-onset, and continue doing these, sometimes for many hours per day, after other abilities and interests are lost. The current study demonstrates that skill at jigsaws amongst SD cases is not confined to (a) conventional puzzles with rectangular outside edges and colour continuity between pieces, nor (b) SD patients with a passion for jigsaws. A cohort of SD cases completed puzzles at speeds comparable to age-matched controls and faster than patients with Non-Fluent Progressive Aphasia (PNFA). A series of 7 experimental puzzles, varying from a simple 10-piece one through a 19-piece scrambled photograph to a 14-piece one-colour puzzle with an irregular shape, showed a significant group by condition interaction: the SD group completed the scrambled photo in fewer moves than the PNFA and control groups, and the most difficult jigsaws in no more moves than controls. Despite SD patients' profoundly diminishing ability to understand the world around them, their visuospatial skills and concentration appear to be maintained or even enhanced in solving jigsaw puzzles.