AbstractWe are interested in those bundles C on ℙN which admit a resolution of the form0 → ℂs ⊗ E $$ \buildrel\mu\over\to $$ ℂt ⊗ F → C → 0.In this paper we prove that, under suitable conditions on (E, F), a generic bundle with this form is either simple or canonically decomposable. As applications we provide an easy criterion for the stability of such bundles on ℙ2 and we prove the stability when E = 𝒪, F = 𝒪(1) and C is an exceptional bundle on ℙN for N ≥ 2. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)