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Is it easier for brokers to find shares to short in premarket?
The shares available to short are a portion of those shares held by the longs. This number is actually much easier to determine outside of active trading hours, but either way doesn't really impact the matter at hand since computers are pretty good at counting things. If your broker is putting up obstacles to your issuing sell short limit orders in the pre-market then there is likely some other reason (maybe they reserve that function to "premium" account holders?)