The reduced model for the flow of a large ice sheet is uniformly valid when the bed topography is flat or has slopes relative to the horizontal of order no greater than ϵ , where ϵ 2 is a very small dimensionless viscosity based on the geometry and flow parameters. The reduced model is given by the leading–order balances of an asymptotic expansion in ϵ. Real ice–sheet beds will have much greater slopes, of order unity in places, but commonly of moderate magnitude, say σ = 0.2, corresponding to 11°, over large regions. The length s over which a moderate slope extends may be as small as the sheet thickness, or considerably greater, subject to the restriction that the amplitude a = σ s of the local topography does not exceed the sheet thickness. Then, in addition to ϵ, there are two further independent parameters from the trio ϵ , s and a . An asymptotic expansion is constructed for steady plane linearly viscous isothermal flow over bed topography, such that ϵ ≪ ≪ 1, and the leading–order terms, an enhanced reduced model, are determined explicitly. First–order correction terms are also determined explicitly when s is much greater than the sheet thickness. Examples are computed in the latter case for a variety of bed forms involving isolated moderate–slope zones, and for a wavy–bed form of moderate slope. Comparisons between the leading–order solutions and the standard reduced–model flat–bed solutions are made, and the effects of the first correction terms are shown. It is found that moderate bed slopes with linearly viscous isothermal flow do not induce a significant correction, so that the enhanced reduced model provides a good approximation.