Smectic-A liquid single crystal elastomers (S-A-LSCE) are materials where the rubber elasticity of the polymer network is combined with the one-dimensional positional long-range order of mesogenic groups which are covalently attached to the network. In the systems investigated so far, a mechanical deformation of the network causes significant reorientation processes of the layered structure. We present a new type of S-A-LSCE in which this structure remains unaffected on mechanical deformation both parallel and perpendicular to the director. The thermoelastic behavior, macroscopic dimensions, and stress-strain measurements parallel as well as perpendicular to the director are investigated. X-ray studies confirm that a deformation parallel and perpendicular to the layer normal does not alter the macroscopically ordered lamellar structure with respect to the order parameter and the layer correlation length. We propose a simple picture where defects within the lamellar structure might account for these findings.