RINGHORNE  Be sure to enter the "mac" folder; I would check here only:

ftp.logitech.com/pub/techsupport/mouse/mac

There should not be any .exe files in there.   
(Version 2.4)

RINGHORNE  Go to ftp.logitech.com/pub/techsupport/mouse/mac as that should have the LCC version you seek.

WARNING: I added a wireless keyboard to a wired mouse I have had for years. To clarify, both were Logitech. LCC gave me no trouble with the mouse, ever. Then the kybd was freezing my whole darn system! I tried all types of things to try to keep the problems from occurring, including downloading and installing older versions of the LCC, and nothing worked.

I got rid of the Logitech keyboard - no joke. Instantly, the mouse worked EXACTLY as it should with the LCC software. My new keyboard is NOT Logitech, and is wireless and works fine.

Logitech is far lower on my list of device makers now. That kybd problem was a MAJOR headache!  
(Version 2.4)

RINGHORNE  You can find older versions of the Logitech Control Center software on their ftp site. ftp.logitech.com/pub/techsupport/keyboards or choose the /mouse subdir. One or the other is where I found it.  
(Version 2.4)

RINGHORNE  I began using ByteCon .6 and it worked smoothly, as good as I could want. For the longest time, it was one of my startup items, when I was doing a lot of iTunes listening. Version .6 had only minor issues that never hurt the actual function (its buttons were at times inconsistent -- play-pause mode icons reversed). This is an EXCELLENT tool: simple, flexible (can pick from many looks), complements my tasks with ease when I am on two monitors and iTunes is hidden. No iTunes butting in my space, and no getting in the way of other menus!  
(Version 0.8.6)

RINGHORNE  SORRY! Not 2.1.0, but 2.0. Logitech Control Center 2.1.3 is no good for many. Best to go all the way back to version 2.0 via the FTP site noted in my prior (and others') posting.  
(Version 2.1.3)

RINGHORNE  I believe this will solve issues for many with problems posted here. That is, forget 2.1.3 and go back three steps. At least users of 10.3.9, maybe higher and lower OS releases: Get v. 2.1.0 from the company FTP site at

ftp://ftp.logitech.com/pub/techsupport/mouse/mac

(Thanks user "Serge," for getting FTP location from Logitech and posting it here, though they told you to get 2.1.1.) Download "lcc20.dmg" file. (Yes, it will manage mouse and keyboard.)

To summarize my own waste of time: Versions 2.1.3, 2.1.2, 2.1.1, all did not work for me. I am running 10.3.9, using a G3 PowerBook. I had problems with all above noted versions until I loaded 2.1.0. It is fine, dare I say, perfect. And my original version didn't work (one that came with my keyboard a while back).

And may Logitech one day explain what was supposed to be useful in the later versions, but not listed in their documentation. Someday?  
(Version 2.1.3)

RINGHORNE  You are signt on, Serge. Thanks for the fpt address. Geez! I remember in the old days you didn't have to search and search for that kind of info!!! Hopefully it will allow me to use my shortcuts, etc.   
(Version 2.1.3)