Although the interest on half-metallic Heusler alloys, susceptible to be used in spintronic applications, has considerably grown, their interfaces with semiconductors show very low spin-polarization. I identify mechanisms which can keep the high spin-polarization at the interface (more than 80% of the electrons at the Fermi level are of majority spin) although the half-metallicity is lost. The large enhancement of the Cr moment at the interface between a CrAl terminated Co2CrAl(001) spacer and the InP(001) semiconductor weakens the effect of the interface states resulting in this high spin-polarization. On the other hand the Co2CrAl/InP interfaces made up by a Co layer and either an In or a P one show a severe decrease of the Co spin moment but Cr in the subinterface layer is bulklike and the resulting spin-polarization is similar to the CrAl-based interfaces.