4-Hydroxy-2-cyclobutenones, which are readily obtainable from diethyl squarate, reacted with lead tetraacetate to give 5-acetoxy-2(5H)-furanones and 5-alkylidene-2(5H)-furanones via oxy-radical-triggered ring opening (beta-scission) and subsequent 5-endo reclosure. This method was extended to saturated four-membered alpha-ketol and applied to the synthesis of a natural product (Z-isomer of multicolanate). A carbon-centered radical-triggered reaction was also performed in which photolysis of a mixed anhydride of thiohydroxamic acid and (4-oxo-2-cyclobutenyl)acetic acid afforded a 4-cyclopentene-1,3-dione rather than the furanone as a rearranged product. The similarity of these rearrangements is discussed using a PM3 calculation in terms of pentadienoyl radical to cyclopentenone radical cyclization and its oxa version.