Phase estimation algorithm

I have a problem with implementating the phase estimation algorithm. It is a problem I have run into many times before. Namely that this algorithm requires a control-U gate. The only way to decompose a gate U (in order to turn it into a controlled gate is e^ialphaAXBC (where of course A,B,C are parametrized standard gates). The problem, again, is that the phase shift e^ialpha cannot be implemented, which means that the whole result eventually won't make sense. This same problem has held me back trying to implement other things. How should I proceed?

(I'll assign it to Matthias, mainly so that I am sure you'll see this problem)