The polytropic stellar model with index n = 0 has a uniform density distribution throughout, and consequently its physical radius is essentially arbitrary because the surface density condition, ϱ = 0, is never satisfied. This surface anomaly, which is not associated with the other polytopic models for 0 < n ≤ 5, could be a constraining factor in certain astrophysical applications involving the n = 0 polytrope. For example, in some circumstances it may be appropriate to utilize the simple physical formulation of the model but on the other hand inappropriate to disregard any zero boundary requirements for the surface density. A sequence of new E-type (as defined below) composite analytical solutions to the Lane-Emden equation, based on the indices 0 and 1, has been developed which eliminates this physical indetermination. The associated polytropic models can be classified as essentially uniform density models. Specifically, they have a large central uniform density n = 0 zone matched, in a physically consistent way, to a small outer n = 1 zone which has a steep density gradient giving ϱ = 0, along with T = 0 and P = 0, at the radial distance corresponding to the first zero of the composite solution.