How do you reduce or prevent excessive drinking at a BYO house party?!

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It'll all end in tears, the only way to have a good party is to control the numbers.

I'd tell them straight out : "Hey dude...I'm having a party, drinking's allowed, but not to excess out of respect for my parents...if anyone gets out of hand, we'll have to ask them to leave."

Then get a couple of your really good friends who think like you do and will stand by as "bouncers". The longer a party lasts, the more drinking that goes on. Watch out for serious trouble-makers>>they can ruin a party. It's up to you to look out for the other guests who DO respect the fact of how you're conducting your party. And try to invite only those guests whose behavior you can trust if at all possible.

First question: Is 18 the legal drinking age in your state? If no, then no booze, Sorry.

You could have everyone who shows up check their car keys with Mom or Dad - and they don't get them back if they're not judged sober enough to drive (NOTE: this can have legal implications for Mom & Dad, though).

Have really big ice cubes, lots of fresh juice and real home made sweetmeats, bread and cheese.
Have the guests put their bottle with the rest at the "bar" with the "barkeep" Spruce it up with signs ,, music and your best.

I agree with ladydi. You could also ask an aunt or uncle to play designated driver and take your party-goers home. If they're not cool with that arrangement (having to be brought back to their cars the next day) then no drinky-drinks for them.