Nope, I'm not with any wildlife system. I'm with the rock. The one that dares to be different. I am, so it seems, the only one dumb enough to accept a free system upgrade (Yosemite). Yosemite killed most of my Adobe applications (probably a plan by Adobe to force more people to Creative Cloud).
So the winning answer is below under Related Articles: OS X...
1. Log in using my admin account.
2. Click System Preferences.
3. Select Users & Groups.
4. Click the lock (to unlock).
5. Enter your admin password.
6. Select the relevant user account.
7. Click change password.
I was trying to do this through the Security and Privacy item, which included a Change Password button, but to no avail. Accessing the password through Users & Groups worked nicely.