Lyman made a receiver sight for the 340. They can be found with a bit of searching. Be careful though, the same sight was made for the old Savage M40 Sporter and Super Sporter, with the same part number as for the 340. There is a slight difference in the two. A good sight man (Mad Dog?) can probably clarify that.
The Super Sporter Lyman is called a Model 40, on mine anyway.
My Grandfathers 340 in 222 has a side mount on it and with a K4 and double horozontal crosshair. Shoots very well on paper but try as I might I am sitting at coyotes:3, and Noel:0.
Can't offer what to try for best shooting, they very first load in this one shot so well we never tried any others.
