A new technique called the weighted integration method for the measurement of local CBF (LCBF) in humans with positron emission tomography (PET) is presented. LCBF is calculated from weighted time integrals of the blood and tissue radioactivity curves. This method is computationally efficient and achieves nearly optimal statistical estimation of LCBF. The predicted root mean squared error of the weighted integration method is verified by simulation studies and is only 1-2% larger than the minimum possible error that can be achieved by an ideal estimation algorithm. For LCBF of greater than 30 ml/min/100 g, the weighted integration method provides reduced noise compared with the integrated projection technique, the PET autoradiographic method, and the steady-state technique. In addition, an error analysis is performed to study the sensitivity of the weighted integration method to tissue mixtures, blood sample timing errors, and changes in LCBF during the data collection period.