Commonly used soil water retention, θ(h), and moisture capacity, C(h), functions implicitly assume that (i) the θ(h) data curve is sigmoid-shaped with an inflection and (ii) the C(h) data curve has a value of zero at soil saturation. Desorption measurements on intact soils indicate, however, that the θ(h) data curve is frequently convex-monotonic in shape with no inflection, and C(h) at saturation is often a finite negative value rather than zero. As these model-data mismatches may cause substantial error in simulation or prediction of near-saturated soil hydraulic properties and water flow, a new “Extended Schnute” θ(h)–C(h) function was proposed that can provide θ(h) curve shapes and saturated C(h) values which are consistent with θ(h) and C(h) measurements. The new function and/or its nested Schnute sub-model provided high-quality and physically realistic fits to desorption data collected from intact cores of coarse sand, loamy sand, loam, clay loam, sandy clay loam, clay, and organic clay soils; and it out-performed or equalled the three-parameter van Genuchten θ(h)–C(h) function for every data-set. The new function also provided accurate and physically realistic representations of θ(h) and C(h) data from structured soils containing macropores and strongly graded pore size distributions. It was concluded that the Extended Schnute model is capable of providing accurate and physically realistic representations for a wide range of θ(h) and C(h) data, and it was further recommended that this model be considered over other models when measurements indicate that θ(h) is convex-monotonic in shape and/or C(h) is not zero at soil saturation.