We present the strict Fibonacci heap , the first pointer-based heap implementation with time bounds matching those of Fibonacci heaps in the worst case. Strict Fibonacci heaps support make-heap, insert, find-min, meld and decrease-key in worst-case \(O(1)\) time, and delete and delete-min in worst-case \(O(\lg n)\) time, where \(n\) is the size of the heap. The data structure uses linear space. A previous solution achieving the same time bounds in the RAM model made essential use of arrays and extensive use of redundant counter schemes to maintain balance. Our solution uses neither. Our key simplification is to discard the structure of the smaller heap when doing a meld, and to use the pigeonhole principle in place of the redundant counter mechanism to maintain balance.