Computing Euclidean Distances is a very important operation in digital communication, especially in the case of trellis coded modulation, where it is used numerously. This paper shows that a substantial reduction in complexity can be achieved in hardware processing elements for computing Euclidean Distances. A reduction in complexity down to 39% is shown compared to traditional designs. The paper also shows that the optimized design can be done completely ripple free, which leads to a reduction of the critical path to far more than half. The reduction in complexity leads to a reduction in power consumption. The ripple free design also leads to lower power consumption for two reasons: the rippling in itself leads to unnecessary glitches, which costs power and the shorter critical path enables a lower supply voltage, which reduces the power consumption as well. © 2011 IEEE.