One of the most crucial stages of the Mars exploration missions is the entry, descent, and landing (EDL) phase. During EDL, maintaining reliable communication from the spacecraft to Earth is extremely important for the success of future missions, especially in case of mission failure. EDL is characterized by very deep accelerations, caused by friction, parachute deployment and rocket firing among others. These dynamics cause a severe Doppler shift on the carrier communications link to Earth. Methods have been proposed to estimate the Doppler shift based on Maximum Likelihood. So far these methods have proved successful, but it is expected that the next Mars mission, known as the Mars Science Laboratory, will suffer from higher dynamics and lower SNR. Thus, improving the existing estimation methods becomes a necessity. We propose a Maximum Likelihood approach that takes into account the power in the data tones to enhance carrier recovery, and improve the estimation performance by up to 3 dB. Simulations are performed using real data obtained during the EDL stage of the Mars Exploration Rover B (MERB) mission.