  We study the tensor modes of linear metric perturbations within an effective
framework of loop quantum cosmology. After a review of inverse-volume and
holonomy corrections in the background equations of motion, we solve the
linearized tensor modes equations and extract their spectrum. Ignoring holonomy
corrections, the tensor spectrum is blue tilted in the near-Planckian
superinflationary regime and may be observationally disfavoured. However, in
this case background dynamics is highly nonperturbative, hence the use of
standard perturbative techniques may not be very reliable. On the other hand,
in the quasi-classical regime the tensor index receives a small negative
quantum correction, slightly enhancing the standard red tilt in slow-roll
inflation. We discuss possible interpretations of this correction, which
depends on the choice of semiclassical state.
