A transition from Ising criticality to mean-field tricritical behaviour was concluded lately for the ternary system of NaBr in mixtures of water and 3-methylpyridine from light-scattering measurements (J. Jacob et al., Phys. Rev. E, 1998, 58, 2188). In this paper we report for this ternary system measurements of the phase diagram, of the line of lower critical points and of the critical viscosities for a set of concentrations of the salt in the range of 10–19 mass%. The critical line is found to depend linearly on the salt content without noticeable discontinuity. The viscosity measurements yield Ising criticality at all concentrations of the salt. The critical exponent found is y = νz = 0.0398 ± 0.0007 (i.e.z = 0.0632) in accordance with the expectations [0.041 (0.065)] for an Ising system, while a vanishing of the critical divergence at a tricritical point was expected. Crossover to non-critical behaviour is observed, which is well described by the mode-coupling theory. While the value of the exponent is not influenced by the content of the salt, the cut-off wave number and hence the amplitude of the critical viscosity assume a minimum at compositions where the reported light-scattering measurements suggest mean-field tricriticality.