Information-theoretic measures based upon mutual information can be employed to quantify the information that an execution of a program reveals about its secret inputs. The information leakage bounding problem asks whether the information leaked by a program does not exceed a given threshold. We consider this problem for two scenarios: a) the outputs of the program are revealed, and b) the timing (measured in the number of execution steps) of the program is revealed. For both scenarios, we establish complexity results in the context of deterministic boolean programs, both for programs with and without recursion. In particular, we prove that for recursive programs the information leakage bounding problem is no harder than checking reachability.