Link-based data structures, such as linked lists and binary search trees, have many well-known rearrangement steps allowing for efficient implementations of insertion, deletion, and other operations. We describe a rearrangement primitive designed for link-based, heap-ordered priority queues in the comparison model, such as those similar to Fibonacci heaps or binomial heaps. In its most basic form, the primitive rearranges a collection of heap-ordered perfect binary trees. Doing so offers a data structure control on the number of trees involved in such a collection, in particular keeping this number logarithmic in the number of elements. The rearrangement step is free from an amortized complexity standpoint (using an appropriate potential function).