  We present a series of theoretical constraints on the potentially viable
inflation models that might yield a blue spectrum for primordial tensor
perturbations. By performing a detailed dynamical analysis we show that, while
there exists such possibility, the corresponding phase space is strongly
bounded. Our result implies that, in order to achieve a blue tilt for
inflationary tensor perturbations, one may either construct a non-canonical
inflation model delicately, or study the generation of primordial tensor modes
beyond the standard scenario of single slow-roll field.
