Application of quantum chemical methods to molecules of chemical interest requires expansion of (one‐particle) wavefunctions by basis functions. For many computer programs in quantum chemistry, it is economically advantageous to use so‐called segmented contracted sets, for which atomic shells are not fitted as a whole, but by segments. This scheme, which allows but also requires certain flexibility in the choice of the number of contracted functions, is explained in detail in this chapter. For the description of correlation there are well known schemes for the consistent extension, derived from the contributions of functions to the total correlation energy in post‐Hartree‐Fock (HF) methods. The chapter discusses the special aspects arising for lanthanides from the ‘missing’ inner electrons when using effective core potentials, from the presence of the partly occupied f shell, the flexibility of the 6s/5d/4f occupation, and the comparably close energetic distance of the 6p shell.