Can I optimize a left join for a single match?

Consider a join A LEFT JOIN B ON A.id = B.a_id:

• B.a_id is nullable -- most but not all B records point to an A record.


• A can, at most, only have one matching B record (business logic).


• Not all A records have a match in B.

Is there a way to tell MSSQL that there will never be more than one A:B match, thus allowing it to shortcut the join once a match is found for a given A record?

I would think that such an optimization could happen if B.a_id had a unique index, but that's not possible since it's nullable.

Complicating the issue: A and B are in different databases (same MSSQL instance).

If it matters, I'm using SQL Server 2008 R2.