We propose a sequential optimization technique for segmenting a rectified image of a facade into semantic categories. Our method retrieves a parsing which respects common architectural constraints and also returns a certificate for global optimality. Contrasting the suggested method, the considered facade labeling problem is typically tackled as a classification task or as grammar parsing. Both approaches are not capable of fully exploiting the regularity of the problem. Therefore, our technique very significantly improves the accuracy compared to the state-of-the-art while being an order of magnitude faster. In addition, in 85% of the test images we obtain a certificate for optimality.