An experimental technique to measure simultaneously the thermal diffusivity and thermal conductivity of small specimens of thermal-insulator materials is described. Experimental conditions are developed which approach the mathematical idealization of a one-dimensional, infinite, two-component, composite solid whose planar interface is subjected to a step-function heat flux. The heat flux is generated by resistive heating of a thin metallic foil. Although this principle has been exploited previously, the present technique permits specimens with volumes two orders of magnitude smaller than prior work based on the same idealization. A number of difficulties related to small specimen volume are identified and overcome. Another improvement over past efforts is the use of the nonlinear least-squares analysis to determine the optimum values for diffusivity and conductivity. A comparison of measurements of these properties for acrylic and Pyrex glass with literature values suggests that the technique affords accuracies of about 5% for materials in this range.