Rear drumb breaks

I have a 86 Caprice wagon. I just replaced the rear breaks. When the car hits 63Mph to 70 Mph the rear starts to shake. There is no vibration in the steering wheel. I have re-balanced the tires, and rotated, no help. I never had a problem like this. I have put 30K miles on it recently.

Any chance the new break drumb is out of ballance? I even ran the car with the rear wheels off the ground. 63+Mph and the shake would start.

Please offer any ideas. I have a 1000 mile trip to go on in a day, and would like to go over 60 MPH!

Hi,I am wondering if it gets worse when you apply the brakes.Heres a simple way to check to see if your drums are warped.Find a nice smooth length of road w/ no traffic or parking lot.Coast your car at about 20 mph and gently gradually apply your park brake untill you come to a complete stop.If it stops smooth your drums are true.If it is jerky or pulsating your drums are warped.Could also be u joint (vibration usually accompanied w/ humming noise) Good Luck!