We present a new coherence functional to evaluate quantitatively the goodness of waveform fit between two time series as function of lag time. The proposed coherence measure is called phase cross-correlation (PCC) because it is based on the similarity of instantaneous phases. No amplitudes are explicitly involved, and PCC is therefore an amplitude unbiased measure, which equally weights every sample in the correlation window. As consequence PCC enables to discriminate between closely similar waveforms and is suited to detect weak arrivals that are concealed in larger amplitude signals. Besides, for signal recognition PCC can be applied for arrival time picking, as a misfit function, or it can be used in combination with stacking techniques. The performance of PCC is illustrated and discussed in comparison with the conventional cross-correlation normalized with the geometric mean energy. Both measures are based on different concepts, and the differences in their performance can be significant. The choice of the proper coherence measure depends on the data and application. We show in a data example the ability of PCC to detect weak P-to-s conversions in the P-wave coda of teleseismic events. With this example we give confirming evidence for a crust that is thicker than the global average and for the existence of the 410-km and 660-km discontinuities underneath SE Brazil. In addition, we observe hints of a 510-km discontinuity.