Minimization does not necessarily change the severity level of a problem, but in most cases minimal problems are harder than their "normal" origin.
Both, newly generated problems and existing problems can be minimized. The former is controlled by the respective option, the later can be enforced either by selecting the menu entry "Problem|Find Minimal Allocation" or by pressing <F9>.
Currently normal Sudokus with only 17 pre-allocations and X-Sudokus with only 12 pre-allocations are known.