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Harmonia Axyridis
16 spots on this one, red body, with convergent white spots on its pronotum.
Yard
Thanks again! Your comment prompted me to do some research, and you are absolutely right. We have them down here everywhere now, and they look quite similar to native species. They're causing a big stir with pet owners here, because they attach themselves to the roofs of dogs' mouths and cause serious pain and damage.
Hippodamia convergens has a more oblong body shape and different markings. See here: http://bugguide.net/node/view/8374
Harmonia axyridis is quite variable in color and pattern. The round body shape and color pattern seems to match your beetle a bit closer. :-)