Here is a history of 4001 and 4003 production, composed of information
   from the sources given below:

      4001 - '61 to '80 (or possibly as late as '81)

      4001S - '61 to '69, '80 to '84

      4003 (1st version) - '80 (or '81) to '84 
                                    truss-rod adjuster at body end
                                    two-piece pickguard

      4003 (2nd version) - '84 to '95
                                    truss-rod adjuster at headstock end
                                    one-piece pickguard

      4003S (1st version) - '81 to '84 
                                    truss-rod adjuster at body end
                                    two-piece pickguard

      4003S (2nd version) - '84 to current
                                    truss-rod adjuster at headstock end
                                    one-piece pickguard

   ["The Bass Book" by Bacon and Moorhouse, as quoted by
    Matthew Thallmayer, iconoclast@erols.com, 3/12/1998]
   [Chris Capozza, growlyman@aol.com, 3/12/1998]

   "The 4001 ended sometime during 1980, maybe even '81. That overlaps too, 
    but that's the difference between the catalog or price list dates which 
    reflect inventory, and actual production dates.  Without a doubt there 
    are even a few 4001's with later serial number dates, which would been 
    'stragglers' through the production process or 'clear off the shelf'
    goods."

   [John Hall, ceo@rickenbacker.com, 3/13/1998]

   "The string tension of a round wound string, especially a nearly
    pure iron string like those in the Roto Sound class, is almost 100
    lbs. greater than a typical flat wound string.

    The 4001 neck was designed in 1956 for the only type of strings
    available then . . . flat wound . . . and since the design favored
    a slim neck, the neck strength was right on the edge of the
    envelope. Round wound strings took many of these instruments
    beyond their rated capability for string tension, resulting in
    various problems. But of course there are many types of strings,
    not to mention that every piece of wood is different, so plenty of
    4001's have been used with round wound strings for decades with no
    ill effect.

    The best advice on these older basses is to use the light tension
    string you can stand.

    The 4003 has a completely different truss rod design and can handle 
    any type of string you prefer.

    Fretwire has nothing to do with any of this, as we've always used the
    hardest alloy available. But it is true that a round wound string will 
    tend to wear down any bass's frets faster."

   [John Hall, ceo@rickenbacker.com, 12/17/1998]