In data exchange, data are materialised from a source schema to a target schema, according to suitable source-to-target constraints. Constraints are also expressed on the target schema to represent the domain of interest. A schema mapping is the union of the source-to-target and of the target constraints. In this paper, we address the problem of containment of schema mappings for data exchange, which has been recently proposed in this framework as a step towards the optimization of data exchange settings. We refer to a natural notion of containment that relies on the behaviour of schema mappings with respect to conjunctive query answering, in the presence of so-called LAV TGDs as target constraints. Our contribution is a practical technique for testing the containment based on the existence of a homomorphism between special "dummy" instances, which can be easily built from schema mappings. We argue that containment of schema mappings is decidable for most practical cases, and we set the basis for further investigations in the topic. This paper extends our preliminary results.