The hydroacoustic monitoring of suspended sediment concentration (SSC) in rivers is based on the inversion of backscatter and attenuation models. To evaluate such models, acoustic backscatter and attenuation were measured from a homogeneous suspension of fine river sediments (clay) in a laboratory tank at various concentrations in the range 1-18~g/l. Agreement between the modelled and measured acoustic backscatter and attenuation values was found to be relatively poor. The results are highly sensitive to particle size and shape which come with large measurement uncertainties and they can be significantly improved by adjusting plausible particle parameters. Various inversion methods combining single or multiple frequencies, analysis of backscatter and/or attenuation, spherical or oblate shape hypothesis for particles and fixed or estimated lognormal grain size distribution are tested. The most promising inversion methods using both backscatter and attenuation information led to accurate SSC estimates.