Georeferencing a Lambert conformal conic

I'm trying to georeference a map (a non-referenced tiff) which is (I'm pretty sure) in a Lambert conformal conic projection. Digitizing four control points at the four corners produces a map which is correct along the N-S longitude edges but which "sags" along the lines of latitude.
What method/workflow should I use to do this correctly? Should I just digitize lots of points along lines of latitude and do a polynomial rectification or is there a simpler way?
What method/workflow should I use to do this correctly? Should I just digitize lots of points along lines of latitude and do a polynomial rectification or is there a simpler way?
Comments
Let me know if I can be of further assistance.
Thanks,
Mike
Global Mapper Support
support@globalmapper.com
Then, I tried using my best guess as to the reference projection and two (NW and SE) corner points using the automatic method. That didn't work at all. However, when I added the two other corner points, the rectification on automatic worked fairly well although still not perfectly, but close enough for my purposes.
Thanks again!