  An infinite-$U$ term is introduced into the Holstein-Primakoff-transformed
magnon hamiltonian of quantum Heisenberg magnetic models of spin $s$. This term
removes the unphysical spin wave states on every site and truncates
automatically the expansion in powers of the magnon occupation operator. The
resultant strong-coupling magnon hamiltonians are accurately equivalent to the
original spin hamiltonians. The on-site $U$ levels and their implications are
studied. Within a simple decoupling approximation for our strong-coupling
magnon models we can easily reproduce the results for the (sublattice)
magnetizations obtained previously for the original spin model. But our bosonic
hamiltonians without any unphysical states allow for substantially improved
values for the spectral weight in the ground state and for lower ground-state
energies than those obtained within previous approximations.
