Encoders of AOM/AV1 codec consider an input video sequence as succession of frames grouped in Golden-Frame (GF) groups. The coding structure of a GF group is fixed with a given GF group size. In the current AOM/AV1 encoder, video frames are coded using a hierarchical, multilayer coding structure within one GF group. It has been observed that the use of multilayer coding structure may result in worse coding performance if the GF group presents consistent stillness across its frames. This paper proposes a new approach that adaptively designs the Golden-Frame (GF) group coding structure through the use of stillness detection. Our new approach hence develops an automatic stillness detection scheme using three metrics extracted from each GF group. It then differentiates those GF groups of stillness from other non-still GF groups and uses different GF coding structures accordingly. Experimental result demonstrates a consistent coding gain using the new approach.