The hyperelastic behaviour of an elastomer is typically modelled using strain-energy functions (SEFs) that describe the stress-strain response. SEFs have received attention for unfilled and filled rubbers. Studies on the latter often consider tyres or vibration dampers. The present work is motivated by highly filled oilfield sealing materials. Such compounds exhibit a rapid reduction in low strain modulus and most hyperelastic models cannot fully capture this effect. The problem is illustrated by fitting existing SEFs to stress-strain data for oilfield rubbers. A modified first invariant based Amin-Alam-Okui SEF (2002) which is a generalisation of the Yeoh SEF (1990) is proposed to model this rapid reduction in modulus without compromising the ability to simulate finite-extensibility. This SEF captures low strain inflections in uniaxial compression, a phenomenon that has been observed in previous publications. Stability considerations are discussed and the SEF is implemented in Abaqus for a 3-D general strain problem.