The moving frame of reference technique is modified so that the unobserved cross-beam wind components can be retrieved, with high resolution, from data measured by either single-Doppler or conventional radar. In this modified algorithm the reflectivity fields detected by consecutive radar scans are used to find a moving frame of reference for which the reflectivity measurements are as stationary as possible. After interpolating all of the observational data onto this optimal moving frame and assuming that the wind field is in a steady stare for several radar scans, one can formulate a cost function that contains the following weak constraints: 1) conservation of reflectivity; 2) a geometric relationship between the radial velocity V-r and its Cartesian components u, v, w; 3) incompressibility; and 4) small vertical vorticity. By minimizing this cost function, a complete three-dimensional wind field can be constructed. Using simulated data to test this method against the original moving-frame technique, it is found that the retrieval results are improved significantly. The modified method can sustain different sources of errors. This property is needed if the application of this method to real Doppler radar datasets is desired. When only reflectivity data are available, the modified method can still catch the principal feature embedded in the true wind field, which implies that the utility of a conventional radar-if equipped by this modified method-might be promoted further. Finally, the computation is economical, which is important for operational purposes. Overall, the modification proposed in this study substantially increases the moving-frame technique's applicability.