Programmer - SQL join against date ranges?

Programmer Question

Consider two tables:

Transactions, with amounts in a foreign currency:

     Date  Amount
========= =======
 1/2/2009    1500
 2/4/2009    2300
3/15/2009     300
4/17/2009    2200
etc.

ExchangeRates, with the value of the primary currency (let's say dollars) in the foreign currency:

     Date    Rate
========= =======
 2/1/2009    40.1
 3/1/2009    41.0
 4/1/2009    38.5
 5/1/2009    42.7
etc.

Exchange rates can be entered for arbitrary dates - the user could enter them on a daily basis, weekly basis, monthly basis, or at irregular intervals.

In order to translate the foreign amounts to dollars, I need to respect these rules:

A. If possible, use the most recent previous rate; so the transaction on 2/4/2009 uses the rate for 2/1/2009, and the transaction on 3/15/2009 uses the rate for 3/1/2009.

B. If there isn't a rate defined for a previous date, use the earliest rate available. So the transaction on 1/2/2009 uses the rate for 2/1/2009, since there isn't an earlier rate defined.

This works...

Select 
    t.Date, 
    t.Amount,
    ConvertedAmount=(   
        Select Top 1 
            t.Amount/ex.Rate
        From ExchangeRates ex
        Where t.Date > ex.Date
        Order by ex.Date desc
    )
From Transactions t

... but (1) it seems like a join would be more efficient & elegant, and (2) it doesn't deal with Rule B above.

Is there an alternative to using the subquery to find the appropriate rate? And is there an elegant way to handle Rule B, without tying myself in knots?