Temperature-dependent, in-plane, thermoelectric power data are presented for single crystals of Ba(Fe1−x Cox )2As2 (0 ≤ x ≤ 0.05) and Ba(Fe1−x Rhx )2As2 (0 ≤ x ≤ 0.171). Given that previous thermoelectric power and angle resolved photoemission spectroscopy studies of Ba(Fe1−x Cox )2As2 delineated a rather large Co-concentration range for Lifshitz transitions to occur, and the underdoped side of the phase diagram is poorly explored, new measurements of thermoelectric power on tightly spaced concentrations of Co, 0 ≤ x ≤ 0.05, were carried out. The data suggest evidence of a Lifshitz transition, but instead of a discontinuous jump in thermoelectric power in the range 0 ≤ x ≤ 0.05, a more gradual evolution in the S(T) plots as x is increased was observed. The thermoelectric power data of Ba(Fe1−x Rhx )2As2 show very similar behavior to that of Co substituted BaFe2As2. The previously outlined T–x phase diagrams for both systems are further confirmed by these thermoelectric power data.