A fast multipole method (FMM) for asymptotically smooth kernel functions (1/r, 1/r^4, Gauss and Stokes kernels, radial basis functions, etc.) based on a Chebyshev interpolation scheme has been introduced in [Fong and Darve, 2009]. The method has been extended to oscillatory kernels (eg. Helmholtz kernel) in [Messner et al., 2011]. Beside its generality this FMM turned out to be favorable due to its easy implementation and performance based on intense use of highly optimized BLAS libraries. However, a bottleneck has been the precomputation of the M2L operator and its higher computational intensity compared to other FMM formulations. Here, we present several optimizations for that operator, which is known to be the most costly FMM operator. The most efficient ones do not only reduce the precomputation time by a factor of more than 1000 but they also speed up the matrix-vector product. We conclude with comparisons and numerical validations of all presented optimizations.