Imagine a model of a dead leaf to be scattered on some grass. This model looks like a flat-ish bowl, because dead leaves are usually concave on one side. But falling leaves can land both upright or upside down.
I think Horizontal Mirroring randomly flips scattered objects along x and y. So how about flipping along Z? Certainly, flipping along Z does not make sense for trees, but it might work well for things like leaves and rocks and add just that much more randomness.