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My soviet-era Russian bike is shimmed so it can use a standard headset. I forget the exact sizes but I think it had a 30.4mm headtube ID instead of the usual 30.2mm. I just held the strip of shim in place to get it started, then the shoulder on the headset cup did the rest.
Plus plenty of grease according to my build thread, but the pics are dead, unfortunately: https://www.lfgss.com/conversations/275811/
I haven’t had to touch it since. That bike is my daily and it’s probably got around 6000 miles on it since fitting.
Annoying, but salvageable.
https://rover.ebay.com/rover/0/0/0?mpre=https%3A%2F%2Fwww.ebay.co.uk%2Fulk%2Fitm%2F263851756171
[stupid link sharing convoluted hyperlink - sorry]
Buy that, which is 0.05mm. Cut a strip with some good sharp scissors, a little longer than the depth of the cup and just under one complete turn. Press the cups in with the shim.