Upper limits from previous imaging surveys (DODO survey from Hogan et al. 2011, HST/NICMOS studies from Debes et al. 2005a) for substellar objects around white dwarfs. The only positive detection so far is WD 0806-661B, but it is not shown because the separation is 2500 au (Luhman et al. 2011). We also include the upper limit on GD 50 from Spitzer/IRAC studies (Farihi et al. 2008). GD 50 is the most distant white dwarf in the figure, and yet our limit on GD 50 is still the most stringent.