One of the goals of the Mantle Electromagnetic and Tomography (MELT) Experiment is to determine whether a narrow zone of enhanced melt concentration consistent with focused upwelling exists beneath the East Pacific Rise. Using SKKS, sScS, and S phases from two intermediate-depth earthquakes in the Banda Sea and the Tonga-Kermadec region, we demonstrate that there is no positive evidence for the existence of such a zone and that travel time delays for shear waves traveling through it must be <0.5 s. To test whether diffraction and wave front healing could obscure evidence for its existence, we employ a pseudospectral method to simulate finite frequency teleseismic waves propagating through narrow, vertical low-velocity zones. A rich set of reflected, diffracted, and guided waves is generated when S waves encounter such a low-velocity channel, particularly at high frequencies. Limiting the frequency content to the lower-frequency bands with good signal-to-noise ratios in the observed phases obscures these waveform complexities. The travel time anomaly is broadened and reduced in amplitude but remains detectable unless the low-velocity zone is very narrow or has only modest velocity contrast. The lower limit of detectability corresponds to a 5-km-wide channel of partial melt extending from 10 to 60 km below the seafloor at the ridge axis with a shear velocity contrast of 0.5 km/s. Although these limits are severe, 3 to 4% melt retention might cause a large enough viscosity reduction and anomalous buoyancy to dynamically focus upwelling into a 5-km-wide channel that falls within the limits. Strongly focused, dynamic upwelling beneath the ridge, however, is probably not compatible with the existence of a broad region of very low shear velocities in the surrounding mantle.