Realising cosmological models in string theory, by for instance embedding inflation models in a string compactification, typically requires to have a metastable de Sitter background. The latter would correspond to e.g. the vacuum at the end of inflation. Here we focus on classical backgrounds: those only contain well-controlled ingredients to realise the embedding as a compactification. Such de Sitter solutions are very difficult to obtain, and there exists so far no metastable example. We study this problem and as a first step, we derive new constraints on the existence of classical de Sitter solutions, considering various configurations of D-branes and orientifolds. While some configurations completely forbid having de Sitter solutions, others still allow for it in small regions of the parameter space that we identify.