The article is devoted to optimization of the mean-square approximation procedures for iterated Ito stochastic integrals of multiplicities 1 to 4 based on multiple Fourier-Legendre series. The mentioned stochastic integrals are part of strong numerical methods with convergence orders 1.0, 1.5, and 2.0 for Ito stochastic differential equations with multidimensional non-commutative noise. We show that the lengths of sequences of independent standard Gaussian random variables required for the mean-square approximation of iterated Ito stochastic integrals can be significantly reduced without the loss of the mean-square accuracy of approximation for these stochastic integrals.