Abstract We investigate the realization of a nonsingular cosmological bounce in metric f ( R ) gravity using a controlled exponential deformation of the Starobinsky R2R^{2} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:msup mml:miR</mml:mi> mml:mn2</mml:mn> </mml:msup> </mml:math> model. Adopting a smooth Gaussian-type bouncing scale factor, we first demonstrate a no-go result showing that a positive-curvature vacuum bounce cannot be supported by the model $$f(R)=R+\alpha