In molecular optimal control theory a laser pulse is designed to drive a molecular system to a target value of an observable. To be feasible in the laboratory, the optimal electric field must have a finite amplitude. Current algorithms limit the maximum amplitude indirectly by constraining the field's energy. We introduce a trigonometric mapping for the field amplitude to limit the maximum amplitude explicitly. In a calculation with hydrogen fluoride we show that an explicit amplitude constraint is particularly important when we account for the electric field's effect on the electronic structure. (c) 2005 Elsevier B.V. All rights reserved.