A new stereospecific rearrangement of the saturated cyclobutanones (10a and b) and (11a and b) to the respective bridged cyclopentanones (2a and b) and (5a and b) using triethyloxonium tetrafluoroborate is described. Rearrangement studies of the specific labelled ketone [2H2]-(10a) indicate that the process is intramolecular. Sulphuric acid-catalysed rearrangement of (10a) produces the unsaturated methyl ketone (13). Transformation of the tetracyclic ketones (5a and b) to some angularly functionalised hydrofluorene synthons (14a and b) to the C20-gibberellins has been achieved.