Abstract: A dynamically compensating counterbalance enables a numerically controlled contouring head to maintain proper balance through large slide travels, cutting tool radial travels, and weight changes in the cutting tool at high speeds. A counterweight within the contouring head moves oppositely to the slide direction by means of a pair of interconnected fluid cylinders. Slide reciprocation under numerical control pumps the first cylinder to slave the second cylinder and the counterweight connected thereto. The counterweight is of a high density material, thereby enabling the counterweight to have lesser and proportional travel than the corresponding slide travel while maintaining proper counterbalance. Proportional slide and counterweight travels are accomplished by employing cylinders of an unequal areas. The invention includes a servo operated third cylinder in fluid communication with the first and second cylinders.