An ultrasonic Doppler flow (e.g. blood) imaging and/or measuring system capable of adaptively suppressing stationary or slowly-moving non-flow (e.g. tissue) signals having variable spectra from the recovered ultrasonic echoes. In accordance with the invention, the tissue signals are suppressed using a tissue rejection filter arrangement having an attenuation characteristic which is controlled based upon measured estimates of at least one spectral characteristic of the tissue signals to be removed, thereby maximizing the rejection of tissue movement signals and minimizing undesired attenuation of the blood flow signals. In accordance with an embodiment of the invention, signal routing out of the corner-turning buffer memory component in prior art systems is advantageously modified, so as to provide during a first mode of operation, the echo signal data to a Doppler velocity processor, for forming estimates of tissue signal motion. These estimates are then used for developing a control signal for application to a tissue motion rejection filter arrangement. During a second mode of operation, the echo signal data are provided to the same Doppler velocity processor, however, this time via the tissue motion rejection filter arrangement. Thus, the estimates of tissue signal motion are developed in a simplified hardware arrangement, by using the same corner turning memory and Doppler velocity processing circuitry as is used for developing the blood flow velocity signals.