Orient your map to the magnetic north of the compass and then shoot your azimuth.
If the map is not sufficiently recent, the map's idea of magnetic north will be different from the compass's idea of magnetic north, and you're back to making an adjustment.
shoot two azimuths to recognizable landmarks and draw lines on your map using the edge of the compass
And if you draw a third line, from a third point, chances are you have a small triangle rather than a point.
I'd only assume a compass is accurate to about 1-2 degrees even if it has markings for additional precision. I believe the spec for the military ones is markings at 20 mils, with a max error of 40 mils (i.e. 2.25 degrees).

