The dual-Doppler analysis of the vertical velocity field in convective storms has long been fraught with difficulty. One of the main problems stems from the inevitable loss of low-altitude wind/convergence information due to beam blockage, ground clutter, and (non-zero) height of beam above ground. Our work focuses on a new method of dual-Doppler wind analysis, with an emphasis on improving the retrieval of the vertical velocity field in the presence of substantial low-level data voids. The analysis proceeds in a three-dimensional variational (3DVAR) framework with the anelastic form of the vertical vorticity equation imposed along with traditional constraints of mass conservation and smoothness. The local derivative term in the vertical vorticity equation is estimated with the Taylor frozen turbulence hypothesis (space to time conversion). Preliminary tests of the algorithm provided encouraging results with analytical data (a Beltrami flow solution of the Navier-Stokes equations). Here we describe recent analyses of dual-Doppler data of a tornadic supercell storm that occured on 10 May 2003 in central Oklahoma. Comparisons will be made between (i) a traditional analysis in which the impermeability condition is imposed but the vorticity constraint is not considered, (ii) a vorticity-equation based procedure in which the impermeability condition is not imposed, and (iii) a combined vorticity equation and impermeability condition approach. The dual-Doppler wind analyses are complemented with a polarimetric variable analysis that reveals an interesting correspondence between enhanced ZDR values and an unusual updraft pattern.