  We study power utility maximization for exponential L\'evy models with
portfolio constraints, where utility is obtained from consumption and/or
terminal wealth. For convex constraints, an explicit solution in terms of the
L\'evy triplet is constructed under minimal assumptions by solving the Bellman
equation. We use a novel transformation of the model to avoid technical
conditions. The consequences for q-optimal martingale measures are discussed as
well as extensions to non-convex constraints.
