I only saw the 'small circle' near Callanish III for the first time on my recent trip. Everyone seems to assume that it must be prehistoric because it's near the stone circle. And I'm not saying it isn't the remains of an ancient cairn. But it looks like a possible beehive house to me. These were used as shielings (temporary summer homes while looking after cattle on the moor) in relatively recent times.
Thom was confused by a simlar but larger ring of stones and named it Callanish VII. A 'nearby ruin' which he mentioned was definitely a beehive house. I have a 1904 photo of it still with its corbelled roof. By the sheep fanks (pens) on the hillock across the road from Callanish IV, a beehive house has been reconstructed by my old friend Jim Crawford (who also did the Bosta Iron Age House reconstruction - a must when visiting Lewis - and the Land Agitation Cairns). He used the 1904 photo to help in the reconstruction.
Against my sheiling theory - it's a bit close to Callanish village for a sheiling (airigh in Gaelic) - they were usually well out in the moors.