TEAM 40X
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If your Trigger looks like the diagram below then there is hope for a nice 20oz trigger.
Or less if you want to experiment.

40X Trigger

Remove all the adjusting screws and springs. Be careful you do not lose the little ball bearing when you remove the "Trigger Adjusting Screw" - the spring might send it flying.
No Screws you say? Most of the time Remington fills up the screw holes with wax or something so the Lawyers are happy. Just carefully dig around a little with a pick to expose the screw heads and the top of the trigger adjusting screw stake.
Next you want to flush out all the oil, grease and other junk with lighter fluid.  If you have some aerosol brake cleaner then hit it hard with that first.  Then use some lighter fluid.  Go ahead and give it a good soaking. Do not oil the trigger the lighter fluid will take care of that.

After you get it clean go ahead and put a little oil on the screws and spring. Lets put the trigger adjusting screw, spring and bearing in first. Adjust it so the it just barely holds in the bearing. Now put an empty case in the chamber and close the bolt. It should stay cocked.
(you never want to dry fire a good rimfire)
Now put in the trigger engagement screw and slowly tighten until the sear releases and the firing pin drops. Now try backing out the this screw 1/3 turn. Re-cock the bolt and see if the sear stays engaged. You can also see this by looking through a hole at the top center of the trigger.
If the firing pin drops when you close the bolt then try backing out the screw another 1/4 turn and repeat the above.
Now lets work on weight of pull. If it is still way too heavy then you can try cutting a coil off the spring.
Do not cut so much that the trigger will not positively return! Now put in the trigger stop screw and adjust it so you have very little over travel after the sear releases.  (Turn in till it is snug and back-out 1/4 turn usually works)
Now go back and readjust (fine tune) the trigger engagement screw you might even be able to turn it in a little.
If I made sense on all of the above & you understood what I was saying you should now have a nice 20 to 30 oz trigger.
Make sure you do some 'Thump and Bump' tests to insure it does not fire. Do these with the safety on and off. Open and close the bolt a few times between bump tests to make sure it stays cocked and does not slam fire. BE SAFE - TEST - and TEST AGAIN!
Remington makes a great trigger.  If you now want to get serious about Benchrest Shooting then get a Jewel.  You will never regret it!
Doug
Some Downloads:
Decode the Date
40-XB Field Service Download Manual
40-X Range Master Download Manual
40-X Parts Manual Download PDF
40-X Bolt & Trigger Download PDF