We are interested in those bundles on P that admits a resolution of the form 0 → C ⊗ E φ −→ C t ⊗ 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 P and we prove the stability of all Steiner exceptional bundle...