  We consider the directed percolation process as a prototype of systems
displaying a nonequilibrium phase transition into an absorbing state. The model
is in a critical state when the activation probability is adjusted at some
precise value p_c. Criticality is lost as soon as the probability to activate
sites at the first attempt, p1, is changed. We show here that criticality can
be restored by "compensating" the change in p1 by an appropriate change of the
second time activation probability p2 in the opposite direction. At
compensation, we observe that the bulk exponents of the process coincide with
those of the normal directed percolation process. However, the spreading
exponents are changed, and take values that depend continuously on the pair
(p1, p2). We interpret this situation by acknowledging that the model with
modified initial probabilities has an infinite number of absorbing states.
