PBW bases for a class of braided Hopf algebras

We prove the existence of a basis of Poincare-Birkhoff-Witt type for braided Hopf algebras R generated by a braided subspace V of P® if the braiding on V fulfils a triangularity condition. We apply our result to pointed Hopf algebras with abelian coradical and to Nichols algebras of low dimensional simple U_q(sl_2) modules.