Registry Refers To Nonexistent Java Runtime Environment Installation

I was having trouble running some Java programs (not my own) in Windows XP, and in the process I uninstalled and installed JRE versions 6, 7, and 8, one at a time, probably in the order 7, 8, 7, 6, 7. The program that had the original problem only worked in V6, but some other programs stopped working. I went back to V7, and those other programs still didn't work. The message was "the registry refers to a nonexistent java runtime environment installation". The only advice I could find with Web searches was to reinstall the JRE. Needless to say, that didn't work.
 
So I looked at the registry, and I found that there were still references to V8, which had been uninstalled. The first was
 
HKEY_CLASSES_ROOTjarfileshellopencommand - (Default) = "C:Program FilesJavajre1.8.0_31binjavaw.exe" -jar "%1" %*
 
The folder re1.8.0_31 doesn't exist, so I changed it to jre7. That didn't work.
 
Then I found
 
HKEY_LOCAL_MACHINESOFTWAREJavaSoftJava Runtime Environment - CurrentVersion = 1.8
 
I changed this to 1.7, and deleted some following entries such as
 
HKEY_LOCAL_MACHINESOFTWAREJavaSoftJava Runtime Environment1.8 - JavaHome = C:Program FilesJavajre1.8.0_31
 
retaining entries such as
 
HKEY_LOCAL_MACHINESOFTWAREJavaSoftJava Runtime Environment1.7 - JavaHome = C:Program FilesJavajre7
 
That worked!
 
So, there is a bug in the installer(s): if you uninstall V8 and install V7, the 'CurrentVersion' isn't set correctly, with the result that the registry points to a non-existent folder. The V8 uninstallation should delete these entries, or the V7 installation should change them.