SJT is a natural ideal strictly contained within the ideal of K-trivial degrees.  We have been hearing about a number of results connecting the K-trivials with notions of randomness.  For example, the covering problem which states that every K-trivial is computable from a difference random.  Many of these results have analogs for SJT; for example, every SJT is computable from a Demuth random.  I will present SJT and its parallels with K-triviality.