Wounded, Old, and Lecherous

This is all valuable advice, except that it makes no mention at all of the sauce-maker's most important tool - the stick blender (immersion blender, wand blender, hand blender or Bermixer). If you don't have one you don't know what you're missing.

Lump-free roux can be made with warm (not too hot) oil and flour and an HB.

Good (not the best, but pretty good) white (Bechamel) sauce can be made by whizzing flour, full cream milk and a little melted butter and then bringing to the boil and simmering for about a minute, for Veloute replace the milk with your stock.

There is no real reason to add the flour to the dish when making gravy - put the deglaze liquid and the flour in a beaker and whiz it with your HB then carry on as before. Guaranteed lump-free!

The general rule is that if you have to cook the flour in fat whiz them together if you can, but expect lumps if you can't (you won't get 'em if you're good, but nobody's perfect), and if the flour is only to be cooked once the liquid has been added whiz everything before cooking. This also removes the necessity for careful mashing and sieving of potatoes or suchlike.

Whether or not the starch is cooked an HB will remove lumps without the need for sieves, second bowls, or the evacuation of the kitchen. The only problem is when there are lumps you want (bits of meat, vegetable, etc.) and also lumps of cooked starch which you don't - the only solution to that is to blend the lot and pretend you meant to have non-chew sauce.