We address the issue of generating texts in the style of an existing author, that also satisfy structural constraints imposed by the genre of the text. We focus on song lyrics, for which structural constraints are well-defined: rhyme and meter. Although Markov processes are known to be suitable for representing style, they are difficult to control in order to satisfy non-local properties, such as structural constraints, that require long distance modeling. We show that the framework of Constrained Markov Processes allows us to precisely generate texts that are consistent with a corpus, while being controllable in terms of rhymes and meter, a result that no other technique, to our knowledge, could achieve to date. Controlled Markov processes consist in reformulating Markov processes in the context of constraint satisfaction. We describe how to represent stylistic and structural properties in terms of constraints in this framework and we provide an evaluation of our method by comparing it to both pure Markov and pure constraint-based approaches. We show how this approach can be used for the semi-automatic generation of lyrics in the style of a popular author that has the same structure as an existing song.