On big tilting modules with a small orthogonal class

We investigate bounded complexes T , with projective components, corresponding to partial tilting modules, say X , big enough to inherit from tilting modules a functorial condition on the kernels of all Hom and Ext functors. As a consequence, theses modules X have the following property: (+) Every simple module S occours as an epimorphic image of a submodule M of X . Under suitable assumptions concerning - the orthogonal class associated to X ; - possible complements of X , as a direct summand of a tilting module; property (+) implies that X satisfies the functorial Hom-Ext condition verified by tilting modules. Finally,we construct more or less complicated indecomposable bounded complexes C , with projective components, such that any morphism from T to any shift complex C[i] is homotopic to zero.