First I discuss low-threshold stagnation problems in the GMRES iterative solver. I show how to alleviate them in certain situations. Then I turn to the main topic of the talk – a method to enhance the efficiency of integral equation based schemes for elliptic PDEs on domains with corners, multi-wedge points, and mixed boundary conditions. The key ingredients are a block-diagonal inverse preconditioner 'R' and a fast recursion, 'i=1,...,n', where step 'i' inverts and compresses contributions to 'R' from the outermost quadrature panels on level 'i' of a locally 'n'-ply refined mesh. From an efficiency point of view, this method converts a non-smooth boundary into a smooth boundary and mixed boundary conditions into pure boundary conditions. The spectral properties of the system matrices in the linear systems that eventually have to be solved are essentially the same. The "corner difficulties" are gone. The talk is available as a pdf-file: http://www.maths.lth.se/na/staff/helsing/corners.pdf