off the cuff

The etymology of the phrase suggests two possible origins:

• In the times when gentlemans' shirts still had removable collars and cuffs, after-dinner speakers were in the habit of jotting down last minute notes on their shirt cuffs.
• It is also suggested that waiters also used their cuffs when taking orders, but I find this less plausible - they would run out of space very quickly! In a similar vein, merchants in the olden days may have made impromptu transaction records on their cuffs: A casual, "cash" transaction may well have been kept "off the cuff".