The number of strands for a minimum-loss litz-wire winding may be found by evaluating the tradeoff between proximity-effect losses and dc resistance. Of the factors leading to increased dc resistance in a litz-wire winding, only the space allocated to strand insulation varies significantly with the number of strands in a well designed construction. A power law can be used to model insulation thickness in the region of interest. Combining this with standard models for eddy-current loss results in an analytic solution for the optimal number of strands. The simplest model for loss, using only the first terms of a series expansion can be used since good designs use strands that are small compared to a skin depth. Experimental results correlate well with the simple model. Stranding for minimum loss may lead to many strands of fine wire and thus excessive expense. Minimum loss designs constrained by minimum strand size or maximum number of strands have also been derived.