In the context of nonlinear regression models, a new class of optimum design criteria is developed and illustrated. This new class, termed ΙL-optimality, is analogous to Kiefer's Φk-criterion but is based on predicted variance, whereas Kiefer's class is based on the eigenvalues of the information matrix; L-optimal designs are invariant with respect to different parameterisations of the model and contain G- and D- optimality as special cases. We provide a general equivalence theorem which is used to obtain and verify ΙL-optimal designs. The method is illustrated by various examples. Keywords:Bayesian design; Invariance; Optimal design.