Slow unidirectional shift registers can be used to realise a large-size inexpensive stack. A simple configuration of such a shift-register stack will frequently force a processing unit needing access to it into an idle state. In the letter, a scheme using a small number of fast bidirectional shift registers appended to a unidirectional shift-register stack is suggested. This configuration makes the entire stack look, for most of the time, as if it were made of fast bidirectional shift registers. A design method is presented to determine the number of bits needed in the bidirectional shift register to meet given specifications.