Car is '73 1.7 with stock FI. When I go down a hill in 3rd or 2nd gear or when I back off the gas, this thing sputters and loud pops, sometimes with a real Ka-pow!
I have checked and timing seems to be OK. Plugs are not all black and fouled. All of the vacuum lines are pretty new and tight.
What else can I check?
Last compression chk by mechanic showed:
#1 100 psi
#2 120
#3 120
#4 150
Are these wide range of compression numbers telling me something about the cause of backfire?
Thanks for the help and replies

I would check for exhaust leaks

If it was a good/correct compression check, then you have problems. 50 psi difference is way out of range. That may not be causing your backfire problem though. I'm going to guess the vacuum advance on the distributor could be sticking.

I thought it might be exhaust leak too, but I checked the connection of the exhaust at the heads and all seem to be tight. No black soot on the surface of any of them.
If vac advance is sticking, is there some way to un-stick it?

Before I'd do anything else I think I'd look at the exhaust flanges and ports very closely. Be sure to use a flashlight and look for soot. Wipe a finger around the exhaust pipes right at the flanges, both at the head and at the muffler.

As far as the distributor advance, I check it with a Mitivac, which is one of those hand operated vacuum pumps. You can take off the distributor cap, and then pull vacuum on the dashpot and make sure it moves smoothly. Alternately, you can just pull the distributor, clean it up and lubricate the advance mechanism.

I would bet on an exhaust leak. If it isn't leaking at the head/exhaust pipe, check to make sure that the ECU adjust knob is not turned all the way counterclockwise (lean idle), that will cause a backfire on deceleration. I know, I learned the hard way
Good luck.

Warrenoliver

Several things: if you had a big enough exhaust leak to make it backfire you would hear it all the time. I would suggest checking the seals on the injectors as air can easily be sucked in and cause the backfires you mention. Check to make sure each injector has the plastic tip to locate the small seal as if it is missing the seal will move around and cause leaks. If the larger outer seal gets hard and cracked from old age they will let air in also.