The third article in this series of publications deals with solving inverse problems of photometry. The matter of reducing the dimension of the original inverse task with excluding insignificant parameters from the equation is considered. The main known ways of identifying those ones having the greatest and least influence over the main characteristics of the equalization results are noted. Their disadvantages are indicated at solving poorly conditioned issues and problems with initial measurements, the actual accuracy of which is unknown. The characteristics of the results include indicators of precision and statistical quality of the equalization. The main indicators its exactness are the average square deviations of the indirect measurements’ residuals, primarily the coordinates of the reference and connecting points. Those of the statistical quality are estimates of the direct and indirect measurements statistical quality equalization, as well as evaluating the mean square error of the weight unit after that. An algorithm was developed to refine the initial weights of direct measurements, identify and first eliminate insignificant parameters based on the analysis of intermediate data of the task being solved. An addition to the algorithm for adjusting the weights of direct measurements during equalization was formulated; it provides identification and secondary screening of insignificant parameters. Experimental approbation of the identified ways is carried out. The necessity of adjusting the weights of indirect measurements was established.