Literature on endogenous growth shows that a polluting economy can grow sustainably and that a double-dividend (or win-win effect) boosting growth is possible. Even with a semi-endogenous growth approach - which occurs when the knowledge stock yield falls below the unit in the production of innovations - what happens to sustainability and the double dividend? This paper presents the first semi-endogenous growth model with pollution which answers this very question. We first illustrate that the dynamics of this economy can be sustainable even if its long-term growth rate is exogenous. To ensure the latter, a knowledge stock yield that is greater than a certain strictly positive threshold is required. We then demonstrate that the double dividend and the Porter hypothesis are impossible. Indeed, the level of support for innovation has no positive impact on the long-term growth rate, and the environmental policy has a negative effect on growth.