Four-wave mixing in high refractive index materials, such as chalcogenide glass or semiconductors, is promising because of their large cubic nonlinearity. However, these materials tend to have normal dispersion at telecom wavelengths, preventing phase matched operation. Recent work has shown that the waveguide dispersion in strongly confining guided-wave structures can lead to anomalous dispersion, but the resulting four-wave mixing has limited bandwidth because of negative quartic dispersion. Here we first show that the negative quartic dispersion is an inevitable consequence of this dispersion engineering procedure. However, we also demonstrate that a slight change in the procedure leads to positive quartic dispersion, resulting in a superior bandwidth. We give an example in which the four-wave mixing bandwidth is doubled in this way.