Watch your email from DL. I get announcements of short term deals using both money and miles just about weekly, and most of them are BE tickets when you read the fine print. Dates may be limited and there often are advanced purchase restrictions.

Do you mean long haul international or include Caribbean, Canada, Mexico, etc.?

Be sure to watch the Mileage Run forum. Some of the deals for tickets paid with money can be purchased using pay with miles (at approximately one cent per mile) and still be good values. In fact, at least one blogger advocates this strongly (and requires a paid subscription to view international deals).