Rice pudding with coconut milk

This came out extremely rich -- perhaps too rich. Next time, I will use light coconut milk, or substitute half of it for low-fat dairy milk.

Cook 1/2 c of dry rice with 3/4 water and half of a cinnamon stick for 15 minutes

Add to the cooked rice:
2 cups coconut milk (maybe use light coconut milk, or substitute some dairy milk)
1 - 2 tsp vanilla
a pinch of ground cardamom
1/4 or 1/2 c sugar (how sweet do you like it?)
a splash of lemon juice
a handful of raisins

Continue simmering the mixture until it is thick enough for your liking (about 20 minutes for me). Stir frequently.