Last second cruise information

Wanted to know will the cruise lines discount open rooms on their ships. I'm looking at a cruise that leaves next week, I think the deal is good but can I wait even longer and get a better deal. I figure the cruise lines would rather lower the price even more instead of letting the room go empty. I know I'm running the risk of the ship getting booked but I'm thinking it might be worth the risk. When would be the best/last chance I should wait to get the best price? Should I go thru a travel agent/ on line/ cruise line directly? Any info ould be appriciated. This will be my first cruise. Thanks Tim