Constitutive models facilitate investigation into load bearing mechanisms of biological tissues and may aid attempts to engineer tissue replacements. In soft tissue models, a commonly made assumption is that collagen fibers can only bear tensile loads. Previous computational studies have demonstrated that radially aligned fibers stiffen a material in unconfined compression most by limiting lateral expansion while vertically aligned fibers buckle under the compressive loads. In this short communication, we show that in conjunction with swelling, these intuitive statements can be violated at small strains. Under such conditions, a tissue with fibers aligned parallel to the direction of load initially provides the greatest resistance to compression. The results are further put into the context of a Benninghoff architecture for articular cartilage. The predictions of this computational study demonstrate the effects of varying fiber orientations and an initial tare strain on the apparent material parameters obtained from unconfined compression tests of charged tissues.