Complex model-based tools such as code generators are typi- cally designed as chains of model transformations taking as input a model of a software application and transforming it through several intermedi- ate steps and representations. The complexity of intermediate models is such that testing is more conveniently done on the integrated chain, with test models expressed in the input language. To achieve a high test cover- age, existing transformation analyses automatically generate constraints guiding the generation of test models. However, these so called test ob- jectives are expressed on the complex intermediate models. We propose to back-propagate test objectives along the chain into constraints and test models in the input language, relying on precondition construction in the theory of Algebraic Graph Transformation. This paper focuses on a one-step back-propagation.