Sorting by transpositions is a challenging classic problem proposed in genome rearrangement and recently settled as NP-hard. Although the proven hard to sort -permutations are close to the identity, the historical approach has been to study distant permutations, possible candidates to be diametral. The transposition diameter is a related challenging problem, known only for . We advance the study of both transposition distance and diameter by considering lonely permutations and the union operation. We present tighter bounds for the distance of lonely -permutations, , , , and . We set the current lower bound for the transposition diameter back to and propose an alternative union of lonely permutations contributing to the approach used so far in the literature.