J.C. Mitchell cites in his "Expressive power of programming languages" the result in Riecke's "Fully abstract translations between functional languages" about the call-by-value, call-by-name and lazy versions of the language PCF.
He mentions: In lazy PCF, call-by-name evaluation order is used, but additionally termination is observed using some convergence-testing language primitive.
In general terms, he says, the main results are that call-by-value and lazy PCF are equally expressive (apparently shown in Riecke by means of an abstraction-preserving reduction), and both are more expressive than call-by-name PCF.
The first part, of this previous statement is intuitive. The second is not yet to me.
EDIT: Removed some nonsense I had written earlier.