Counting networks are a class of distributed data structures that support highly concurrent implementations of shared Fetch&Increment counters. Applications of these counters include shared pools and stacks, load balancing, and software barriers. A limitation of counting networks is that the resulting shared counters can be incremented, but not decremented.

A recent result by Shavit and Touitou showed that the subclass of tree-shaped counting networks can support both increment and decrement operations. In this paper we generalize their result, showing that any counting network can be extended to support atomic decrements in a simple and natural way. Moreover, we identify a broad class of network boundedness properties, that, like the counting property, are preserved by the introduction of decrements: if a balancing network satisfies a particular boundedness property for increments alone, then it continues to satisfy that property for both increments and decrements.