In bearing fault diagnosis, ensemble empirical mode decomposition (EEMD) is a reliable technique for treating rolling bearing vibration signals by dividing them into intrinsic mode functions (IMFs). Traditional methods used in EEMD consist of identifying IMFs containing the fault information and reconstructing them. However, an incorrect selection can result in the loss of useful IMFs or the addition of unnecessary ones. To overcome this drawback, this paper presents a novel method called combined modes ensemble empirical mode decomposition (CMEEMD) to directly obtain a combination of useful IMFs containing fault information. This is without needing to pass through the processes of IMF selection and reconstruction, as well as guaranteeing that no defect information is lost. Owing to the small signal-to-noise ratio, this makes it difficult to determine the fault information of a rolling bearing at the early stage. Therefore, improving noise reduction is an essential procedure for detecting defects. The paper introduces a robust process for extracting rolling bearings defect information based on CMEEMD and an enhanced deconvolution technique. Firstly, the proposed CMEEMD extracts all combined modes (CMs) from adjoining IMFs decomposed from the raw fault signal by EEMD. Then, a selection indicator known as kurtosis median absolute deviation (KMAD) is created in this research to identify the combination of the appropriate IMFs. Finally, the enhanced deconvolution process minimizes noise and improves defect identification in the identified CM. Analyzing real and simulated bearing signals demonstrates that the developed method shows excellent performance in extracting defect information. Compared results between selecting the sensitive IMF using kurtosis and selecting the sensitive CM using the proposed KMAD show that the identified CM contains rich fault information in many cases. Furthermore, our comparisons revealed that the enhanced deconvolution approach proposed here outperformed the minimum entropy deconvolution (MED) approach for improving fault pulses and the wavelet de-noising method for noise suppression.