The model of time-dependent Petschek-type reconnection is extended
to take into account first-order corrections with respect to the reconnection rate.
The plasma velocity inside the outflow region turns out to be smaller than the
zero-order Alfvén velocity, and therefore strong reconnection is less effective in
plasma acceleration. The model is also applied to study the effect of incoming
waves on reconnection. We show that incoming waves of Alfvén type, carrying an
electric current that is antiparallel to the initial current in the sheet, increase the
reconnection rate and cause additional acceleration of the plasma, so that this wave
can be considered as a potential trigger.