Rear of my car sways over bump.....

[E30QUEST]

It doesnt matter if the bump is big or small the rear of my recently purchased 1991 325i just sway like the car is pushed sideway.I was thinking shocks but they look and feel very solid to me.The PO put on some KYB dampers that are problably too soft.
My rear tires are bald.Can that be the problem?They're 215/60/14 on stock bottle cap wheels,they look too large for them.IDK,please help!!!!

[sharky]

rtabs, tire pressure, shock mounts

[Dirtbleed]

...and subframe bushings

[Tree18is]

its all well worth the work, do everything while your at it.

Trailing arm bushings, diff mount, sub frame bushings, and shock mounts.

[E30QUEST]

Thanks guys!!!!

[Slangbox]

Haha. I like this advice... essentially "Replace everything in the rear suspension that could possibly wear out."

[E30QUEST]

I just found out what my problem is.The rear shock mount on the left side of the car is so toast you can grab the shock while on the car and shake it and there's no resistance.