Dynamical suppression of telegraph and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>∕</mml:mo><mml:mi>f</mml:mi></mml:mrow></mml:mrow></mml:math>noise due to quantum bistable fluctuators

We study dynamical decoupling of a qubit from non-Gaussian quantum noise due to discrete sources, as bistable fluctuators and $1∕f$ noise. We obtain analytic and numerical results for generic operating points. For very large pulse frequency, where dynamic decoupling compensates decoherence, we found universal behavior. At intermediate frequencies noise can be compensated or enhanced, depending on the nature of the fluctuators and on the operating point. Our technique can be applied to a larger class of non-Gaussian environments.