What you're doing is saying that it's true despite the strength of the evidence, not because of it.

That is true despite one weakness in this case.

This was true despite the fact that the younger boys now did all the hunting for the family.

This was true despite an explicit treaty to the contrary.

This remained true despite price reductions from $35 to $10 per ten pages.

And it remains true despite the Bush administration's unpopularity abroad.

This remains true despite a recent tightening of various rules, experts say.

This is true despite advances in imaging and treatment delivery.

The opposite of the first proposition is true, despite popular myth.

The head seems true to life, despite the Seurat-like dots of paint over the whole surface.