  We present a detailed study of the Equilibriumlike invaded cluster algorithm
(EIC), recently proposed as an extension of the invaded cluster (IC) algorithm,
designed to drive the system to criticality while still preserving the
equilibrium ensemble. We perform extensive simulations on two special cases of
the Potts model and examine the precision of critical exponents by including
the leading corrections. We show that both thermal and magnetic critical
exponents can be obtained with high accuracy compared to the best available
results. The choice of the auxiliary parameters of the algorithm is discussed
in context of dynamical properties. We also discuss the relation to the
Li-Sokal bound for the dynamical exponent $z$.
