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Advanced knowledge of the ice thickness distribution within glaciers is of fundamental importance for several purposes, such as water resource management and the study of the impact of climate change. Ice thicknesses can be modeled using ice surface features, but the resulting models can be prone to considerable uncertainties. Alternatively, it is possible to measure ice thicknesses, for example, with ground-penetrating radar (GPR). Such measurements are typically restricted to a few profiles, with which it is not possible to obtain spatially unaliased subsurface images. We developed the Glacier Thickness Estimation algorithm (GlaTE), which optimally combines modeling results and measured ice thicknesses in an inversion procedure to obtain overall thickness distributions. GlaTE offers the flexibility of being able to add any existing modeling algorithm, and any further constraints can be added in a straightforward manner. Furthermore, it accounts for the uncertainties associated with the individual constraints. Properties and benefits of GlaTE are demonstrated with three case studies performed on different types of alpine glaciers. In all three cases, subsurface models could be found that are consistent with glaciological modeling and GPR data constraints. Since acquiring GPR data on glaciers can be an expensive endeavor, we additionally employed elements of sequential optimized experimental design (SOED) for determining cost-optimized GPR survey layouts. The calculated cost-benefit curves indicate that a relatively large amount of data can be acquired before redundant information is collected with any additional profiles, and it becomes increasingly expensive to obtain further information.