Powell's press conference is in progress and things could conceivably shift at some point, but so far, it's been a good thing for bonds.

Reason being: markets were looking for a read on whether Powell would ratchet up the previous level of hawkishness (seen in the last speech) owing to higher inflation data.  Instead, Powell has stuck to the "data dependent" theme, acknowledged the higher Q1 inflation, acknowledged that this means it will take LONGER to achieve goals, but that is it.  He's not saying it means goals are unlikely to be achieved.  He also explicitly said the next move is unlikely to be a hike.  

Powell still expects to see inflation move back down, but he admits that his confidence in that is lower than it was.  

Even with the qualification, bonds like it.  10yr yields are down more than 9bps at 4.587.  MBS are up just over half a point.