Selecting an actual MIN value instead of NULL in SQL query

From this table:

Select * into #tmp from (
select 'a' A, 'b' B, NULL C union all
select 'aa' A, 'ab' B, 1 C union all
select 'aaa' A, 'bbb' B, 2 C ) x

I'd like to get this result:

A   B   Val
a   b   1
aa  ab  1
aaa bbb 2

That is, take the non-null min value and replace the NULL.

I suppose I could join the table to a filtered version of itself where no nulls appear. But that seems overkill. I thought this might be able to be done in the MIN Aggregate clause itself.

Any ideas would be helpful, thanks!