event logs for application install and uninstall

We would like to be alerted any time a user installs or uninstalls software on their computers (Windows 7).  I have found the event IDs that are supposed to correlate to this: 11707 and 1033 for installation events, 11724 and 1034 for uninstall events.  I believe 7045 may also be helpful for service installation.  However, when I tested this I was not seeing events for everything I would have expected.  Sometimes installing would create an event, and sometimes it wouldn't.  Same with uninstalling.  Am I missing something?  Is this the best way to track the installation of software (I realize we could limit administrative privileges but that's not currently an option) or is there a better way you can recommend?  Thanks!