The low power as a feature of a BIST scheme is a significant target due to quality as well as cost related issues. In this paper we examine the testability of multipliers based on Booth encoding and Wallace tree summation of the partial products and we present a methodology for deriving a low power Built In Self Test (BIST) scheme for them. We propose several design rules for designing the Wallace tree in order to be fully testable under the Cell Fault Model. The proposed low power BIST scheme for the derived multipliers is achieved by: (a) introducing suitable Test Pattern Generators (TPG), (b) properly assigning the TPG outputs to the multiplier inputs and (c) significantly reducing the test set length with respect to earlier schemes. Our results indicate that the total power dissipated during test can be reduced from 64.8% to 72.8%, while the average power per test vector can be reduced from 19.6% to 27.4% and the peak power dissipation can be reduced from 16.8% to 36.0%, depending on the implementation of the basic cells and the size of the multiplier. The test application time is also significantly reduced, while the introduced BIST scheme implementation area is small.