'inverting' a dict

[Irmen de Jong]

Hi
I have this dict that maps a name to a sequence of other names.
I want to have it reversed, i.e., map the other names each to
the key they belong to (yes, the other names are unique and
they only occur once). Like this:

{ "key1": ("value1", "value2"), "key2": ("value3,) }

-->

{ "value1": "key1", "value2": "key1", "value3": "key2" }

What I'm doing is using a nested loop:

dict2={}
for (key,value) in dict1.items():
     for name in value:
         dict2[name] = key

which is simple enough, but I'm hearing this little voice in
the back of my head saying "there's a simpler solution".
Is there? What is it? ;-)

Thanks
--Irmen.