The minimization problem for visibly pushdown automata (VPA) is studied. Two subclasses of VPA are introduced: call driven automata, and block automata. For the first class, minimization results are given unifying and generalizing those present in the literature. Unfortunately, this class shares the drawback of all other classes for which a minimization result is known: it is exponentially less succinct than VPA. The second class, block automata, is introduced to address this problem. These automata are as succinct as VPA. A minimization procedure for them is presented that requires one additional parameter to be fixed. An example of an exponential gain in succinctness is given.