Hm. No mention of Huffman or frequency analysis in the OP, but whatever.

It seems to me that you might get close to what (I think) you now want, without having to to any iterative recalculating, this way:

Calculate your single characters and bigram frequencies. Round the number of single characters up to the next power of 2, and add the N most frequent bigrams where N is the number required to make the number of singles up to that next power of two. Now when you construct your Huffman tree it will be a fully populated, balanced binary tree.

As an alternative, you might sort your singles and bigrams together by frequency and then select the top N most frequent (where N is a power of 2 that suits your requirements) from that combined set to build your fully populated, balanced binary tree.

And finally, you might consider using a heap rather than a tree as it has the same order of complexity for lookups (just as fast), but is a considerably more compact representation in memory, thus meeting your need for compact representation whilst potentially holding a greater number of items in the same space.