At early times in numerical evolutions of binary black holes, current simulations contain an initial burst of spurious gravitational radiation (also called "junk radiation") which is not astrophysically realistic. The spurious radiation is a consequence of how the binary-black-hole initial data are constructed: the initial data are typically assumed to be conformally flat. In this paper, I adopt a curved conformal metric that is a superposition of two boosted, non-spinning black holes that are approximately 15 orbits from merger. I compare junk radiation of the superposed-boosted-Schwarzschild (SBS) initial data with the junk of corresponding conformally flat, maximally sliced (CFMS) initial data. The SBS junk is smaller in amplitude than the CFMS junk, with the junk's leading-order spectral modes typically being reduced by a factor of order two or more.