Slow Sink Drain

[Tenderpaw]

I've got dual sinks in my master bath. One of them drains fine but the other has gotten slower and slower over the 10 years i have been in the house. I took apart and cleaned the traps on both sinks and then re-assembled. On the problem sink, it was even slower than before after i cleaned it. Then I happened to loosen the drain connection where the trap connects to the drain in the sink and the water drained completely down the pipe. I don't want to leave it loose. Any ideas on the fix? Thanks.

Dave