The Energy Efficient Ethernet (EEE) standard (IEEE 802.3az) has introduced some modifications to existing Ethernet standards with the aim of improving energy efficiency in the transmission of data frames. The adopted mechanism is to use different power modes of operation such that a device can be put into a low-power mode when there is no data to transmit and awake it very quickly upon frame arrival. This is expected to reduce energy consumption significantly, especially on low-loaded links. An alternative to EEE, known as Adaptive Link Rate (ALR), was also proposed to improve energy efficiency in Ethernet by dynamically changing the link speed at different traffic loads. ALR reduces the energy consumption because the lower the link speed, the less energy is consumed. However, this option is no longer considered in the EEE standard process. In this work, the potential energy savings of combining both EEE and ALR are explored. The results show that such a combination can further improve the already efficient EEE standard given the different power overheads associated with transitions between the active and idle power modes at different link speeds. This conclusion provides a clear motivation to investigate the combination of EEE and ALR more in detail in further developments.