Adjustable inlet guide vanes (IGVs) and variable speed drivers are known as providing process compressors with an effective regulation all throughout the operating envelope of the machine. A large amount of work exists in literature reporting the successful control of multistage centrifugal compressors by means of IGVs or speed separately, while a few studies document the combined use of both devices and their effect on compressor performance. The present paper details the off-design behavior of a multistage centrifugal compressor equipped with both types of control. It is shown that classical IGVs' advantage in extending the operating envelope of a fixed speed multistage compressor tends to reduce when speed regulation is active too. In this sense, the average level of peripheral Mach numbers inside the compressor may be interpreted as a sort of threshold since it deeply affects the stage mismatching at off-design conditions. This consideration is corroborated by a number of applications in a wide range of design peripheral Mach numbers. Based on those cases, the paper reviews the general effectiveness of the combined regulation, thus outlining some general rules of thumb for the choice of the optimal control device for a multistage centrifugal compressor.