If you just want to adjust the nut it can be done but it takes more work than getting a JANIII and putting it in. It just costs less. If the nut is too high then you remove it. usually a gentle tap with a on the side to crack the glue and a bit ov leverage will get it off clean.
Then put some fine sandpaper (800 is good) on a flat surface and take some thickness off the bottom of the placcy nut by sanding it back and forth. A little at a time is best, keep checking the thickness and to ensure you are doing it flat.
When the nut is the new improved thickness re-attach it as flo said
ALWAYS use superglue as it is brittle and can be removed easily, PVA type glues will form gunk if you try and get the nut off and a good wood glue can bind so hard to the timber that the nut will be impossible to remove if it cracks or you want to replace it. Working in repairs this was THE job i hated most, it is painstaking, tricky and easy to damage a guitar. the worst thing that can happen with superglue is that it crack when you dont wan it leading to a 5 min fix, with good glues it can mean a nighmare if you wnt to change nuts
sorry my little rant, but there is some good stuff there.
really if you can get a JAN, they should be mandatory on all stringed instruments except the hurdy-gurdy