While trying to get a gaddag working, it has ocurred to me that if all the permutations of prefix and suffix are included for each work, then the new sub-tree of the gaddag that has the pivot symbol as its root can be used the same way as a stand-alone dawg would be.

Currently, for example, the word CAT would be in the gaddag as CAT, ACT, AND TAC. The remaining possibility (CAT) is not required for the finding of Scrabble plays, but if it is included, the tree with ` at its root is a DAWG of all the words in the gaddag, and can be used for simple yes/no - is-this-a-word? searches.

Also, if the gaddag is compressed by starting at all the leaf nodes, and combining identical endings working back up a level at a time (rather than starting from the root nodes, and combining the identical bits of the same length), the extra copy of all the words will be almost entirely compressed away.