  We study the current controlled modulation of a nano-contact spin torque
oscillator. Three principally different cases of frequency non-linearity
($d^{2}f/dI^{2}_{dc}$ being zero, positive, and negative) are investigated.
Standard non-linear frequency modulation theory is able to accurately describe
the frequency shifts during modulation. However, the power of the modulated
sidebands only agrees with calculations based on a recent theory of combined
non-linear frequency and amplitude modulation.
