A systematic study of predictions of the interacting boson approximation (I
BA)-2 model leads to the identification of two parameter invariants such th
at calculations with the same values of the invariants yield results that a
re identical in certain cases and show close similarities under a wider set
of conditions. The invariants validate a much-used form of the IBA-2 Hamil
tonian and provide a systematic method to simplify IBA-2 calculations by ch
oosing a truncated Hamiltonian with the same invariant values as more gener
al Hamiltonians.