Are there examples of visa-free travel agreements between countries that have no mutual extradition agreements whatsoever?

I imagine that lack of extradition treaties is somewhat of a hindrance for establishing visa-free travel between countries, on the argument that if (potential) criminals can enter freely (and then do some crime) one should be at least able to get them extradited thereafter. (Of course, visas are not a perfect protection against criminals entering.)

So, are there examples of visa-free travel agreements between countries that have no mutual extradition agreements whatsoever? In particular any such examples involving the US or EU countries?