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 Alfven velocity, and therefore strong reconnection is less
effective in plasma acceleration. The model is also applied to study the ef
fect of incoming waves on reconnection. We show that, incoming waves of Alf
ven type, carrying an electric current that is antiparallel to the initial
current in the sheet, increase the reconnection rate and cause additional a
cceleration of the plasma, so that this wave can be considered as a potenti
al trigger.