I need an algorithm which can be (a bit) slower than the Bresenham line drawing algorithm but has to be a lot more exact. With \'exact\' I mean: every touched pixel should b
If your line is thin and pixels are rectangular (square):

then consider using of voxel grid traversal algorithms, for example, see article "Fast Voxel Traversal Algorithm..." by Woo and Amanatides.
Practical implementation (in grid traversal section)
Answer to comment:
Proper initialization for X-coordinate variables (the same for Y)
DX = X2 - X1
tDeltaX = GridCellWidth / DX
tMaxX = tDeltaX * (1.0 - Frac(X1 / GridCellWidth))
//Frac if fractional part of float, for example, Frac(1.3) = 0.3
example in my answer here