The rule of the shorter term sounds like a useful idea. But in practice it's terribly complicated working out whether it applies to a particular work and particular countries.
For the US and UK it's horrendously complex. Whether the shorter term applies to US works in the UK actually depends on when the copyright expired in the US!
The UK followed the rule of the shorter term until 5 November 1956 when the Copyright Act, 1956 came into force. It then didn't follow the rule of the short term until 1st January 1996 when the Statuatory Instrument 1995 No. 3297 came into force, which brought it back in because of the EU regulation HarryT mentioned.
So: Any US work that was out of copyright before November 1956 is out of copyright in the UK. That is, any work published in the US in 1927 or earlier that didn't have its copyright renewed.
If US copyright laws had remained unchanged, any US works that fell out of copyright in the US on 1st January 1997 or later would also now be out of copyright in the UK. Of course, no works have fallen into the public domain in the US since 1997, nor will until 1st January 2019.
Much interesting info on copyright to be found here