Cleaning tin discoloration on copper/tin lid

Modern stainless steel pans with clad bottoms can be as good as copper pans.  McGee developed a simple technique to test the heat distribution where he fits a piece of paper to the bottom of the pan, placing the pan over a burner and carefully watching how the paper browns.  Thick aluminum, clad bottom stainless, and copper all worked equally well. 

There are differences that relate to the techniques used in cooking.  A thin copper pan is great for melting butter or chocolate straight on the burner.  Modern air-gap wall stainless steel pans hold the heat better and work better for simmering or boiling.  Copper is harder to upkeep.

Pans will develop hot spots, even copper which is the better conductor. Until we get graphite added to the cladding  or some other exotic material to distribute the heat, thickness will matter the most for even heat distribution.

I have read several consumer tests and reviews of pans and they fail to note that thermal conductivity and thickness can both be used in practice to balance the temperature distribution and heat flux in a pan.

You could get yourself a specialized sieve brush - the things are meant for mining sieves but cooking sieves are generally the same size (0.5mm - 1.0mm, the latter being the no. 16 that the first link is talking about). I haven't seen any of these sitting in home kitchens - could be that they aren't effective on cooking sieves, but more likely, cooks just don't know or care that they exist.

For the truly dedicated, you could get yourself a studded sieve cleaner or the similar triangle kind with brushes. These are meant for cleaning really fine sieves, as in flour mill equipment, so whether or not it would be useful to you depends on what kind (mesh density) of sieve you have.

Or, if you could loads of money to blow, you could go all out and get yourself an ultrasonic sieve cleaner. Of course, we're now talking about products that don't even have a list price, so if you have to ask, you can't afford it.

Here's perhaps the most interesting option for those of you at home, though: I noticed companies out there selling rubber balls as sieve cleaners, so I was curious whether or not one could just use an ordinary rubber ball. I happened to have one of those big squishy stress-reliever balls sitting around and gave it a shot on my 8" sieve/strainer that had some sediment stuck on it - and guess what, it works! It's not perfect, it didn't get every last grain out, but I only had to rub the inside a couple of times with the ball to get out the vast majority of "dirt". So there's your "home remedy" for cooks on the cheap.