We study the following cancellation problem over an algebraically closed field 𝕂 of characteristic zero. Let X, Y be affine varieties such that $X × 𝕂^m ≅ Y × 𝕂^m$ for some m. Assume that X is non-uniruled at infinity. Does it follow that X ≅ Y? We prove a result implying the affirmative answer in case X is either unirational or an algebraic line bundle. However, the general answer is negative and we give as a counterexample some affine surfaces.