  We present two strategies for combining dynamical pruning with the
multiconfiguration time-dependent Hartree method (DP-MCTDH), where dynamical
pruning means on-the-fly selection of relevant basis functions. The first
strategy prunes the primitive basis that represents the single-particle
functions (SPFs). This is useful for smaller systems that require many
primitive basis functions per degree of freedom, as we will illustrate for
NO$_2$. Furthermore, this allows for higher-dimensional mode combination and
partially lifts the sum-of-product-form requirement onto the structure of the
Hamiltonian, as we illustrate for nonadiabatic 24-dimensional pyrazine. The
second strategy prunes the set of configurations of SPF at each time step. We
show that this strategy yields significant speed-ups with factors between 5 and
50 in computing time, making it competitive with the multilayer MCTDH method.
