The bootstrap method for quantum mechanics is a powerful tool for computing the energy eigenvalues of a Hamiltonian. However, we point out that a conventional implementation employing the standard bootstrap matrix may be insufficient when the potential contains different types of functions, such as polynomial and exponential terms. In such cases, the standard constraints may not fully capture the relations between the corresponding operator sectors, and the method may fail to reproduce the correct spectrum. A similar problem may arise when evaluating expectation values of operators of different types. This issue can occur in a wide range of systems, including statistical models and matrix models. We propose three possible resolutions to this problem.