Coherent compounding can provide high frame rates and wide regions of interest for imaging of blood flow. However, motion will cause out-of-phase summation, potentially causing image degradation. In this work the impact of blood motion on SNR and the accuracy of Doppler velocity estimates are investigated. A simplified model for the compounded Doppler signal is proposed. The model is used to show that coherent compounding acts as a low-pass filter on the coherent compounding Doppler signal, resulting in negatively biased velocity estimates. Simulations and flow phantom experiments are used to quantify the bias and Doppler SNR for different velocities and beam-to-flow (BTF) angles. It is shown that the bias in the mean velocity increases with increasing beam-to-flow angle and/or blood velocity, whereas the SNR decreases; losses up to 4 dB were observed in the investigated scenarios. Further, a 2-D motion correction scheme is proposed based on multi-angle vector Doppler velocity estimates. For a velocity of 1.1 v(Nyq) and a BTF angle of 75°, the bias was reduced from 30% to less than 4% in simulations. The motion correction scheme was also applied to flow phantom and in vivo recordings, in both cases resulting in a substantially reduced mean velocity bias and an SNR less dependent on blood velocity and direction.