Saturating counters are a newly defined class of generalized parallel counters that provide the exact number of inputs which are equal to 1 only if this number is below a given threshold. Such counters are useful in, for example, self-test and repair units for embedded memories. This paper defines saturating counters for arbitrary threshold values and presents several alternatives for their implementation. The delay and area of the proposed design alternatives are then estimated using a 0.25?m cell library. Finally, we study the behavior of saturating counters when the threshold approaches the number of input bits, i.e., the special case of non-saturating parallel counters.