Although the interest in half-metallic Heusler alloys, likely to be usable in spintronic applications, has grown considerably, their interfaces with semiconductors show very low spin polarization. I identify mechanisms which can keep high spin polarization at the interface (more than 80% of the electrons at the Fermi level 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 that of the CrAl-based interfaces.