Conventional Doppler ultrasound is useful for visualizing fast blood flow in large resolvable vessels. However, frame rate and tissue clutter caused by movement of the patient or sonographer make visualizing slow flow with ultrasound difficult. Patient and sonographer motion causes spectral broadening of the clutter signal, which limits ultrasound's sensitivity to velocities greater than 5-10mm/s for typical clinical imaging frequencies. To address this, we propose a clutter filtering technique that may increase the sensitivity of Doppler measurements to at least as low as 0.52mm/s. The proposed technique uses plane wave imaging and an adaptive frequency and amplitude demodulation scheme to decrease the bandwidth of tissue clutter. To test the performance of the adaptive demodulation method at suppressing tissue clutter bandwidths due to sonographer hand motion alone, six volunteer subjects acquired data from a stationary phantom. Additionally, to test in vivo feasibility, arterial occlusion and muscle contraction studies were performed to assess the efficiency of the proposed filter at preserving signals from blood velocities 2mm/s or greater at a 7.8MHz center frequency. The hand motion study resulted in initial average bandwidths of 175Hz (8.60mm/s), which were decreased to 10.5Hz (0.52mm/s) at -60dB using our approach. The in vivo power Doppler studies resulted in 4.73dB and 4.80dB dynamic ranges of the blood flow with the proposed filter and 0.15dB and 0.16dB dynamic ranges of the blood flow with a conventional 50Hz high pass filter for the occlusion and contraction studies, respectively.