The motivation for this paper is the practical problem of interpreting bi-exponential rate-of-rise curves that are observed during many field piezometric tests. In the authors' previous study, a laboratory W-tube system of water flow through two samples of sand was introduced with an adequate mathematical model. The desired bi-exponential character of water flow was obtained by placing two different samples of sand in separate but connected columns. In the present paper, a so-called inverse problem is solved. The optimization procedure is applied in order to jointly estimate a pair of hydraulic conductivity values based on experimentally recorded bi-exponential rate-of-rise curves. The obtained values of hydraulic conductivities are presented and compared to the values determined from independent constant-head permeability tests conducted for the analyzed sands. The results of this identification procedure varied in accuracy. The mean percent errors between the hydraulic conductivity values measured jointly and independently for the analyzed experimental series were in the range of 8.8 to 37.2%. The discussion presents the restrictions of this interpretational method and suggests further modeling plans.