We report a comparative analysis and theoretical description of the superconducting properties of two spin-valve-valve structures containing the Heusler alloy Co2Cr1−xFexAly as one of two ferromagnetic (F1 or F2) layers of the F1/F2/S structure, where S stands for the superconducting Pb layer. In our experiments we used the Heusler alloy layer in two roles: as a weak ferromagnet on the place of the F2 layer and as a half-metal on the place of the F1 layer. In the first case, we obtained a large ordinary superconducting spin-valve effect ∆Tc assisted by the triplet superconducting spinvalve effect ∆T trip c . In the second case, we observed a giant magnitude of ∆T trip c reaching 0.5 K. An underlying theory based on the solution of the Usadel equations using Kupriyanov-Lukichev boundary conditions with arbitrary material parameters for all layers and arbitrary boundary parameters for all interfaces is presented in Appendix. We find a good agreement between our experimental data and theoretical results. PACS numbers: 85.75.-d, 74.45+c, 74.25.Nf, 74.78.Fk c − T P c and enclose the operational area of the SSV depicted by the shaded rectangle. Here, T AP c and T P care the SC transition temperatures for AP and P configurations, respectively. At a fixed temperature within this rectangle the change of the mutual orientation of magnetizations from AP to P by an external magnetic field yields a full switching between the SC and the normal state of the SSV. Therefore, the width ∆T f ull c of the shaded area in Fig. 1 is the most important parameter of the SSV. It should be noted, that the commonly used condition for the realization of the full switching effect ∆T c > δT c is, in fact, not sufficient. The actually relevant parameter ∆T f ull c is always smaller than ∆T c due to the finite value of δT c , and this difference gets larger the larger the value of δT c is. In the first experimental realization of the full switching between the normal and SC