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A spectral support set for a fNLS soliton condensate is often represented by a finite collection of points (anchors) E in the upper half plane H, connected with each other and\/or with the real axis by some set of (Schwarz symmetrical) arcs. Given a set of anchors E, a natural question is to find a collection of such arcs that produces fNLS soliton condensate of minimal average intensity. That leads to a modification of the well-known Chebotarev\u2019s continuum problem, which consists in finding a continuum K \u2282 C of minimal logarithmic capacity that contains a given set of anchors E \u2282 C. In this talk, we discuss our solution to the modified Chebotarev\u2019s problem, where E and K are subsets of the upper half plane H and where we minimize the Dirichlet energy of H \\ K instead of the logarithmic capacity of K. 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