from what I understand, mesh cleanup fixes problems with bad geometry.
but is there a function by which I can delete all edgeloops in a mesh that don’t contribute to the shape? so Maya turns the mesh into as low rez as possible while retaining the shape....

actually there IS a way of doing that:
but its not found in the cleanup tool.
You need to reduce your mesh:
Mesh -> Reduce[]
Reduce by % is the reduce strength.  50% means that you will have about half of the polycount.
Keep quads will tell maya wether it should keep 4sided faces or if it can turn them to 3sided.
Draging that to one still may produce some 3sided faces - just something you need to beware of.
Face compactness will drive maya to try meatch the face shape. A value of 0 will end up in a really messy looking mesh. So you better leave that as 1.

The other attributes explain themselves. I find the best settings to reduce a complex highpoly mesh
look like this:

Intel Core i7-3930k CPU @3.20GHz(12CPUs); Windows 7 Prof. x64; 32 GB DDR3 RAM; Zotac GeForce GTX580 3GB GDDR5; Asus P9X79 Deluxe; 128GB SSD + 2 TB Samsung HD

awesome, thanks a lot ^_^