A Monte Carlo Potts model has been used to investigate cube-texture strengthening during grain growth in rolled high-purity Ni-tapes. The initial conditions for the simulations have been taken from electron back-scatter pattern (EBSP) orientation maps of already fully recrystallized samples. Experimentally, grain growth leads to an increase in the cube volume fraction to > 95%, accompanied by an approximately ten-fold increase in the grain size. High cube volume fractions can be predicted under a number of conditions, though a small surface energy advantage of just 2% for cube-oriented grains is required to match the texture strengthening to the grain size change. An additional issue of interest is the influence on the grain growth of the large area-fraction of twin boundaries in the fully recrystallized condition. The presence of boundaries with low energy has a strong influence on the simulated microstructural evolution.