I had the same problem with my M44. What I did was put a drop of solder on the top of my front sight and then file it down until it looked just like it was "stock." I colored it with a black marker. Of course I had to go to the range and shoot it and keep filing the sight down until it was hitting where I wanted it too. It was shooting about 8" high at 100 yds. After getting it to shoot pretty much at the point of aim, I only had added approx. 1/32" to the sight. Cheap fix.
Does the number stamped on the top of the front sight blade match the number on the barrel?
You can unscrew the rear sight notch plate and shim it to lower it a bit.
Also worth trying is shimming the receiver. Is the receiver tang flush with the stock or sunken? You can put a common washer under the tang.
Some other suggestions from other posts are to adjust the tightness of the receiver screws and the barrel band screws. The receiver screws should be snug, and the barrel band screws backed off until the top hand guard is just slightly loose, then give each screw a full turn in. At the range you can adjust the barrel band screws in or out a half turn at a time.
Can't speak for anybody else, but about a year ago or so I ordered 3 tall front sights for the M39. They shipped fast, the sights went on without a problem on the one that I replaced. One could fine tune the ht but it worked fine. One I got the wind adjusted the somewhat worn out bore shot very well with Bulg HB. It was real nice not having too "hold low" too group them in the black. With the new front sight it is a snap. I had very good luck with them and fast shipping. If they are out or on backorder that may change things. I would order more than one sight, you don't want too be having too swap the sights around too your other M39s. If you don't have "other M39s" now, you will later. Cheers, John.
Only one m-39 I'm more of a Mauser man my self, but never turn down another fine rifle, especially one with easy to adjust sights! I also ordered a mauser tall front sight, thanks for your input, do you or anyone have issues with Checz Green Steel Case ammo in the m-39? Only 1 out of a box of 20 gets "sticky" to extract,
The Czech ammo is of good quailty, but it may stick in the chamber of your M39 and extraction would be difficult. Throughly cleaning your chamber of any residue, such as dried cosmoline, may eliminate the problem, but if your rifle has a tight chamber, then you might want to pass on the Czech with the laquered case.
Got my front sights WOW excellent Quick and easy to drop in, the M-39 was a breeze and the Yugo was just a second longer both look great, going to try them out this weekend, thanks again for all info, Would use Tenn Gun parts again no question, came in nice zip lock bags to put the origionals in!