Assuming the tumbler is in decent shape, I tighten things up with shims made from annealed feeler gauges. In reality, annealing might not be necessary. I only shim two adjacent flats in the cock. After selecting a feeler gauge that is just a little over sized, I solder it onto one flat and file for a tight fit on the tumbler shaft. Soldering a shim onto an adjacent flat would likely cause a problem with the first soldered joint, so a different approach is advisable. The second shim can be epoxied in place and, again, filed for a tight fit on the tumbler. Alternately, a shim of appropriate thickness can be selected and loose-fit as the cock is installed. Feeler gauges are a great resource for that due to the selection of thicknesses. Trim to width and extra length and test fit to find the correct thickness. For final installation, butt the shim up against the shelf on the tumbler shaft and press the cock on. Once on, trim the excess length off the shim and install the screw. The down side is that a loose shim can be lost if the cock is later removed.
There is a perhaps better approach that had not occurred to me prior to posting this reply. The second over-sized shim could be soldered to the adjacent flat on the tumbler shaft and filed for a snug fit. Think I will try that next time.