We discuss methods of coding information into PA-sets and ML-random sets
(e.g. how to make a given set T-reducible to some PA-set or ML-random set).
Slaman and Kucera used these techniques for PA-sets to provide
a characterization of ideals in the T-degrees for which there is
a low T-upper bound. As a corollary, there is a PA-set which is
a low T-upper bound for the class of K-trivial sets.
In the case of ML-random sets, the situation is naturally more
complicated and the techniques are less powerful.
We survey some results in this area including new developments,
e.g. a result of Barmpalias and Montalban that any K-trivial set
is T-reducible to an incomplete (even low) ML-random set.