Lets say I want to model a cylinder sat on top of a cube, where the cube has a width slightly smaller than the diameter of the cylinder, like in the image below: How would you go about doing this cleanly, all in one mesh, and without any funny faces that nobody can see? I had a go, which involved finding and creating vertices at the intersections of the edges of the two shapes and creating lots of faces using these, but it ended up being a right mess, with edge loops going mental and faces rendering oddly no matter which way round they were told to face. Hopefully someone here will have some idea of how to do this nicely (i.e. nice enough to carry on working on!). I'm a programmer, and if it's not made of boxes, I can't model it :)

Did you try boolean union?

Egad, I didn't expect that to work as well as it did. I've read all sorts of nasty things about boolean operations but that produced something very clean indeed. I wonder how well it will perform when used on a non-toy example, where the objects are lined up by eye rather than having their transforms entered by hand...

Thanks very much Erik :)