In color flow imaging (CFI), the rejection of tissue clutter signal is treated separately from blood velocity estimation by high-pass filtering the received Doppler signal. The complete suppression of clutter is then difficult to achieve without affecting the subsequent velocity estimates. In this work, a different approach to velocity estimation is investigated, based on a statistical model of the signal from both clutter and blood. An analytic expression for the Cramer-Rao lower bound (CRLB) is developed, and used to determine the existence of an efficient maximum likelihood estimator (MLE) of blood velocity in CFI when assuming full knowledge of the clutter statistics. We further simulate and compare the performance of the MLE to that of the autocorrelation method (ACM) using finite-impulse response (FIR) and polynomial regression clutter filters. Two signal scenarios are simulated, representing a central and peripheral vessel. Simulations showed that, by including 3-9 (independent) spatial points, the MLE variance approached the CRLB in both scenarios. The ACM was approximately unbiased only for the central scenario in the clutter filter pass band, then with a variance of up to four times the CRLB. The ACM suffered from a severe bias in the filter transition region, and a significant performance gain was achieved here using the MLE. For practical use, the clutter properties must be estimated. We finally replaced the known clutter statistics with an estimate obtained from low-rank approximations of the received sample correlation matrix. Used in the model-based framework, this method came close to the performance of the MLE, and it may be an important step toward a practical model-based estimator, including tissue clutter with optimal performance.