Generally the 160mm tall cpu heatsinks do not fit in micro-atx, small form factor (sff), or home theater pc (htpc) cases. You mentioned the case has to fit under your desk which suggests a tower case. The case would have to be at least 8 inches (204mm) wide to accomodate a 160mm tall tower style cpu heatsink. Hard to find in a micro-atx case.
There may be additional problems with other components. Please provide a list of components so we can see what we have to work with.