  We analyze priority queues including DecreaseKey method in its interface. The
paper is inspired by Strict Fibonacci Heaps [2], where G. S. Brodal, G.
Lagogiannis, and R. E. Tarjan implemented the heap with DecreaseKey and Meld
interface in assymptotically optimal worst case times (based on key
comparisons). At the end of the paper there are mentioned possible variants of
other structural properties an violations than they have used in the analysis.
In the main variant a lot of information is wasted during violation reduction
steps. Our goal is to concentrate on other variants and to invent natural
strategy not losing that much in the information value. In other words we try
to choose among them one which corresponds to superexpensive comparision
principle as much as possible. The principle was described in [5] of myself,
but after publication I have found these ideas in [4] of H. Kaplan, R. E.
Tarjan, and U. Zwick.
