Not to one up Jay here (sorry joke about another thread). But here is another alternative.

SELECT 

	COALESCE(LTRIM(COALESCE(Salutation,'') + ' ' + FName + ' ' + LName), BusinessName) AS ClientName, 

	A.* 

FROM 

	Clients C

INNER JOIN 

	InvoiceHeader I 

ON 

	I.ClientID=C.ClientID 

INNER JOIN 

	Addresses A 

ON 

	A.ClientID=C.ClientID AND

	(CASE WHEN A.AddrTypeID=@BillingAddressID THEN 1 ELSE A.PrimaryAddr END) = 1

WHERE 

	I.InvoiceNr=@InvoiceNr

The only then that confused me was what

A.AddrTypeID

values are and what

@BillingAddressID

would be. Might have a better example of the code above if I knew that. But I have used this logic before on conditional matching.