Glacier ice thickness is crucial to quantifying water resources in mountain regions, and is an essential input for ice-flow models. Using a surface velocity inversion method, we combine ice thickness measurements with detailed surface elevation and velocity data, and derive ice thickness and volume estimates for the Monte Tronador glaciers, North Patagonian Andes. We test the dependence of the inversion model on surface slope by resampling glacier slopes using variable smoothing filter sizes of 16–720 m. While total glacier volumes do not differ considerably, ice thickness estimates show higher variability depending on filter size. Smaller (larger) smoothing scales give thinner (thicker) ice and higher (lower) noise in ice thickness distribution. A filter size of 300 m, equivalent to four times the mean ice thickness, produces a noise-free thickness distribution with an accuracy of 35 m. We estimate the volume of the Monte Tronador glaciers at 4.8 ± 2 km3 with a mean ice thickness of 75 m. Comparison of our results with earlier regional and global assessments shows that the quality of glacier inventories is a significant source of discrepancy. We show that including surface slope as an input parameter increases the accuracy of ice thickness distribution estimates.