The kinetics of initiation of styrene and butadiene polymerizations by bis(triphenylmethyl)barium (Tr2Ba) and 1,1-diphenylalkylbarium and -sodium were studied. It was found that the initiation efficiency of Tr2Ba is very low in THF but greatly increases when THF is replaced by benzene. The dependencies of initiator efficiency and the MWD of the polymers formed on k(i)/k(p) and M-0/I-0 were investigated theoretically. According to the results obtained, at certain conditions the initiators studied can be considered as suitable for controlled polymerization despite the fact that the basicity of 1,1-diphenylalkyl and, especially, triphenylmethyl carbanions is much lower than that of benzyl and allyl carbanions. The general aspects related to initiation with low basicity carbanions are discussed. In particular, attention was paid to the fact that, besides triphenylmethyl anion, some other low basicity carbanions such as poly (NN-dimethyl acrylamide) and poly(4-vinylpyridine) living chain ends are also capable of initiating polymerization of nonpolar monomers.