Strong G-fibrations and orbit projections

By a strong G-fibration we mean a G-map which has the right lifting property with respect to all G-SSDR-maps (these maps represent an equivariant version of SSDR-maps in the sense of F. Cathey). We show that for any compact Hausdorff group G the following natural projections are strong G-fibrations: G / K → G / H for closed subgroups H and K of G such that K ⊂ H and G / K is metrizable; the K-orbit map E → E / K if E is a metrizable G-space with only one orbit type and K is a closed normal subgroup of G.