Augmentative and Alternative Communication (AAC) systems allow people with disabilities to provide input to devices which empower them to more fully interact with their environment. Within AAC, switch scanning is a common paradigm for spelling where a set of characters is highlighted and the user is queried as to whether their target character is in the highlighted set. These queries are used to traverse a decision tree which successively prunes away characters until only a single one remains (the estimate). This work seeks a decision tree which requires the fewest expected queries per decision sequence (EQPD). In particular, we remove the constraint that the decision tree needs to be a row-item or group-row-item style tree and minimize EQPD. We pose the problem as a Huffman code with variable, integer cost and solve it with a mild extension of Golin's method in "A dynamic programming algorithm for constructing optimal prefix-free codes with unequal letter costs", IEEE Transactions on Information Theory (1998). Additionally, we model the user on the query level by their probability of detection and false alarm to derive their expected performance on the character level given some decision tree. We perform experiments which show that the min EQPD decision tree (Karp) may reduce selection times, especially for timed (single switch) switch scanning.