SmKS waves provide good resolution of outer-core velocity structure, but are affected by heterogeneity in the D″ region. We have developed an Empirical Transfer Function (ETF) technique that transforms a reference pulse (here, SmKS) into a target waveform (SKKS) by: (1) time-windowing the respective pulses, (2) applying Wiener deconvolution, and (3) convolving the output with a Gaussian waveform. Common source and path effects are implicitly removed by this process. We combine ETFs from 446 broadband seismograms to produce a global stack, from which S3KS-SKKS differential time can be measured accurately. As a result of stacking, the scatter in our measurements (0.43 s) is much less than the 1.29 s scatter in previous compilations. Although our data do not uniquely constrain outermost core velocities, we show that the fit of most standard models can be improved by perturbing the outermost core velocity. Our best-fitting model is formed using IASP91 with PREM-like velocity at the top of the core.