Nilpotency class uniquely determines derived length only for class at most three

Statement
Knowing the nilpotency class of a group (with no additional information) allows us to determine the derived length uniquely only if the nilpotency class is at most three. The cases are below:

For a value of nilpotency class $$c > 3$$, the derived length could be any positive integer that is at least 2 and at most $$\log_2(c + 1)$$.