This paper investigates the influence of different three-dimensional multi-mode initial conditions on the rate of growth of a mixing layer initiated via a Richtmyer–Meshkov instability through a series of well-controlled numerical experiments. Results are presented for large-eddy simulation of narrowband and broadband perturbations at grid resolutions up to 3 × 109 points using two completely different numerical methods, and comparisons are made with theory and experiment. It is shown that the mixing-layer growth is strongly dependent on initial conditions, the narrowband case giving a power-law exponent θ ≈ 0.26 at low Atwood and θ ≈ 0.3 at high Atwood numbers. The broadband case uses a perturbation power spectrum of the form P(k) ∝ k−2 with a proposed theoretical growth rate of θ = 2/3. The numerical results confirm this; however, they highlight the necessity of a very fine grid to capture an appropriately broad range of initial scales. In addition, an analysis of the kinetic energy decay rates, fluctuating kinetic energy spectra, plane-averaged volume fraction profiles and mixing parameters is presented for each case.