Plane wave imaging is desirable for its ability to achieve high frame rates, allowing the capture of fast dynamic events, and continuous Doppler data. In most implementations of plane-wave imaging, multiple low resolution image (LRI) frames from different plane wave tilt angles are compounded to form a single high resolution image (HRI) frame, thereby reducing the frame rate. Compounding is a low-pass mean filter that causes attenuation and aliasing to signals with high Doppler shifts. On the other hand, the lateral beam profile and hence the quality of the HRI frames is improved by increasing the number of compounded frames. Therefore, a tradeoff exists between the Doppler limits and beam profile. In this paper, we present a method that eliminates this tradeoff and produces high resolution images without the use of compounding. The method suppresses the off-focus (clutter) signal by spreading its spectrum, while keeping the spectrum of the in-focus signal intact. The spreading is achieved by using a random sequence of tilt angles, as opposed to a linear sweep. Experiments performed using a carotid vessel phantom with constant flow demonstrate that the spread-spectrum method more accurately measures the parabolic flow profile of the vessel and in particular outperforms conventional plane-wave Doppler at higher flow velocities. The spread-spectrum method is expected to be valuable for Doppler applications that require measurement of high velocities at high frame rates.