Having shifted our communication stance from 'may' to 'will' last month [4], the Fed's upcoming POMO schedule offers some insights into the days when shorting (apart from the obvious Tuesdays) will be dangerous (though the BoJ now stuck may require a communication change back to 'may'). We do note that the Fed POMO'd $44 billion out outright Treasury purchases in May (as expected) and plans to do the same in June with $45 billion pegged (strongly suggesting no Taper anytime soon)... it seems next Friday is your first opportunity (though if the last hour is anything to go by... perhaps the Fed's omniptence is being challenged).
There are only 2 days next month when there is not a POMO...
[5]
Source: NYFed [6] [6]