Non-trivial Counterpossibles

A reflection that was triggered by hearing Timothy Williamson give a paper here last weekend at the last ever Arché Modality Workshop.

Some people (classically, Lewis) think any counterfactual with an impossible antecedent is trivially true, and I'm prima facie inclined to agree. But we should be able to distinguish between ones where there appears to be something non-trivial going on, such as:
1. If the square root of 2 were rational, it could be represented as n/m with n, m integers
and ones which don't seem to have this feature, such as:
2. If the square root of 2 were rational, there would be lemonade rivers.

Two options are:
A: to say that the difference between trivial and non-trivial counterpossibles is one of assertability (1 is assertable in many contexts where 2 is not),
B: to say that this difference is a matter of epistemic accessibility (you can know 1 is true without knowing it has an impossible antecedent, whereas this looks doubtful for 2).

But I'm currently wondering whether, in some cases at least, neither assertability nor epistemic access gives the deepest or most insightful characterization of the difference - they may rather be symptoms. For instance, you might think that in some cases it is the existence of some metaphysically interesting connection between states of affairs described in 'A' and 'B' that really explains why a counterpossible conditional 'A []--> B' is non-trivially true. You would then expect this conditional to exhibit the pattern of assertability and epistemic accessibility usually associated with non-trivial counterpossibles, although that behaviour is not what its non-triviality amounts to but rather a sign of it.

(PS For the record, I don't assume there will be the same story to tell in every case about what sort of factor underlies the assertability and accessibility symptoms.)

(PPS I will - hopefully - get round to replying to the interesting comments on my previous post soon ...)