It is often thought that considerations of practicality speak in favour of accepting the principle that if there is no practical alternative to something then that thing is not unjust. I present an argument which suggests that there are in fact practical costs to accepting such a principle, so that on grounds of practicality we perhaps ought to reject it. That argument does not assume that there are any demands of justice which it is impossible to meet, but only that we are very fallible when it comes to knowing what the possibilities are. I then argue that rejecting that principle and embracing a notion of ‘impossible justice’ has positive practical benefits in respect of putting us in a position to respond appropriately to really necessary injustices if there are any.