In this article, models are constructed of the compact jet in GRS 1915+105 during an epoch of optimal data capture. On 2003 April 2, the object was observed in the hard X-ray/soft gamma-ray band (INTEGRAL), hard X-ray band (RXTE), near-IR (ESO/New Technology Telescope) and the Very Long Baseline Array (VLBA) (8.3 and 15 GHz). The source was in a so-called ‘high plateau state’. The large radio flux provides high signal-to-noise ratios in the radio images. Thus, one can image the jet out to large distances (>1015 cm). This combined with the broad-band coverage make this epoch the best suited for modelling the jet. The parametric method that has been successfully utilized in the realm of extragalactic radio jets is implemented. The basic model is one where external inverse Compton (EIC) scattering of accretion disc photons by jet plasma provides the hard X-ray power law. Unlike active galactic nucleus (AGN) jets, it is found that the radio jet must be highly stratified in the transverse direction in order to produce the observed surface brightness distribution in the radio images. Various jet models are considered. The jet power is Q ≈ 3–4 × 1038 erg s−1 if the hard X-ray power-law luminosity is from EIC in the jet and Q ≈ 2–9 × 1037 erg s−1 if the X-rays are emitted from the accretion disc corona. These estimates indicate that the jet power can be as high as 60 per cent of the total X-ray luminosity.