QCD Phase Diagram at small Baryon Densities from Imaginary mu: Status Report

We summarize our recent results for the (T,mu)-phase diagram of N_f=3 QCD. Finding a strong variation of the critical endpoint mu_c with the quark mass m, we point out that an endpoint within reach of experiment requires fine-tuned quark masses. We further discuss the strategy and first data towards extending our results to the physical N_f=2+1 theory.