The signature splitting of the gamma-vibrational band of several Ru, Pd, Xe, Ba, Os and Pt isotopes is analyzed in the framework of the interacting boson model (IBM). The nuclei studied are close to the gamma-unstable SO(6) limit of the IBM and have well-known gamma bands. It is shown that in most nuclei the signature splitting is better reproduced by the inclusion of a three-body interaction between the d bosons. In none of the nuclei evidence for a stable, triaxial ground-state shape is found. (C) 2008 Elsevier B.V. All rights reserved.