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/HG/K→G/H for closed subgroups H and K of G   such that K⊂HK⊂H and G/KG/K is metrizable; the K  -orbit map E→E/KE→E/K if E is a metrizable G-space with only one orbit type and K is a closed normal subgroup of G.