For Panning & river sluicing for gold, the bucket sieve method just lets you process lots of material & we all know that the more material you process the more gold you'll get.
One of the best bits of advice given to me is below.
Others have given me advice over the years about not to sieve down too small or you can lose gold by accidently chucking it out with the bigger stuff the sieve classified.
I've taken it on board(it's paid off well) & you'll rarely see me sieve other than with the bucket.
Whether I pan or sluice - I just use the bucket sieve 10-12mm or 1/2squares & that's as small as I'll classify. Anything bigger should be easy to identify & anything smaller is easy & quick to pan off or easily sluiced.
Happened to me twice now, that I've found larger pieces in my pan that otherwise could have been screened off with a1/4" or 6mm sieve & possibly lost.
Be very thorough in washing your material in the pan - break down any clay, wash any grass roots & insure you get them heavies down to the bottom.
Most of us don't get large pieces often in the pan but when they do turn up they
far out-weigh the fine stuff we usually go home with.
Since using the buckets and Garrett 14 &15" pans, my panning time has gotten quick & recovery increased. Win, win