Certain features in the primordial scalar power spectrum are known to improve the fit to the cosmological data. We examine whether bouncing scenarios can remain viable if future data confirm the presence of such features. In inflation, the fact that the trajectory is an attractor permits the generation of features. However, bouncing scenarios often require fine-tuned initial conditions, and it is only the ekpyrotic models that allow attractors. We demonstrate, for the first time, that ekpyrotic scenarios can generate specific features that have been considered in the context of inflation. © 2019 American Physical Society.