Abstract:We consider two inequivalent truncations of the super D9-brane: the "Heterotic" and the "Type I" truncation. Both of them lead to an N = 1 non-linear supersymmetrization of the D = 10 cosmological constant. The propagating degrees of freedom in the Heterotic and Type I truncation are given by the components of a D = 10 vector multiplet and a single Majorana-Weyl spinor, respectively. As a by-product we find that, after the Type I truncation, the Ramond-Ramond super ten-form provides an interesting reformulation of the Volkov-Akulov action. These results can be extended to all dimensions in which space-time filling D-branes exist, i.e. D = 3, 4, 6 and 10.