A microprocessor includes core logic that operates according to a core clock signal in order to execute program instructions, clock generation circuitry controllable to generate the core clock signal having one of N different possible frequencies, wherein N is more than two, and a control circuit. The control circuit, in response to a request to operate the core logic at a destination frequency, iteratively controls the clock generation circuitry to generate the core clock signal having a new frequency until the core clock signal frequency is the destination frequency. The new core clock signal frequency on each iteration is one of the N different possible frequencies monotonically closer to the destination frequency. The number of iterations is between zero and N−1 depending upon the destination frequency specified and the core clock signal frequency when the request is received.