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If I am not mistaken the Holley number "4160" refers to a series of carbs. In other words you can buy many different size 4bbl carbs that are all 4160 series Holley carbs.
To find out which exact carb you have look for a number on the choke tower. Stamped on it's front should be a number like "LIST-1850" or something.
A Holley carb in the 600cfm range will do fine for a 390. They are not too difficult to tune either.
Had my carb rebuilt a while back. After playing with the adjustments some, still need a little guidance fellas. I've got the idle jacked up a little too much. I know that for sure. It runs at about 1800 on first startup. It idles at about 600 when warmed up. My mix screws are at about 1 1/2 turns each. I have a steady vac reading but can't remember the exact number off the top off my head. When I drive around, and say stop at one or two places, when I come back out, sometimes she has too crank and I have to pump the pedal very lightly to get her to fire up. Any then she seems to stumble ever so slightly and then she will smooth out. My Dad seems to think I may need to adjust the choke setting. (Electric) If set up correct, I would think she would fire up right on every time I hit the key, just like when I first start her for the day, hit the key and she's running good, and without pedal pumping.
Carb is a Holley 4150, 750 cfm, elec choke, vac seconds, dual feed, single pumper. Got clean fresh filters too. Carb is also nice and clean.