Glues for Soft Plastics

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Anyone know of a decent glue that works on the kind of soft plastic that

things like MicroMachines and Heroclix are made from? Both to bond the 
stuff to itself and to harder plastics like styrene and perspex.

I'm trying to re-base some minis and haven't had any luck so far with 
the regularly-available stuff. Have yet to try superglue, but have my 
doubts if it will work based on vague memories.

Any suggestions?

Phil
----
"We gotta get out into Space / If it's the last thing we ever do!" -- 
Captain Tempest, /Return to the Forbidden Planet/
A sentiment echoed by Phil Atcliffe (atcliffe[at]ntlworld[dot]com)