We propose two efficient cooperative access class barring with load balancing (CACB-LB) and traffic adaptive radio resource management (TARRM) schemes for M2M communications over LTE-A. The proposed CACB-LB uses the percentage of the number of Machine-Type Communication (MTC) devices that can only access one eNB between two adjacent eNBs as a criterion to allocate those MTC devices that are located in the overlapped coverage area to each eNB. Note that an eNB is a base station of LTE-A. In this way, the proposed CACB-LB can achieve better load balancing among eNBs than CACB, which is the best available related work. The proposed CACB-LB also uses the ratio of the channel quality indication that an MTC device received from an eNB over the number of MTC devices that attach to the eNB as a criterion to adjust the estimated number of MTC devices that may access the eNB. As a result, the proposed CACB-LB can have a better set of barring rates of access class barring than CACB and can reduce random access delay experienced by an MTC device, which is also applicable to user equipment (UE). After an MTC device successfully accesses to an eNB, the eNB needs to allocate radio resources for the MTC device. In addition, the proposed TARRM allocates radio resources for an MTC device based on the random access rate of the MTC device and the amount of data uploaded and downloaded by the MTC device in a homogeneous MTC device network, and the priority of an MTC device in a heterogeneous MTC device network. Furthermore, we use the concept from cognitive radio networks such that if there are unused physical resource blocks (PRBs) of UEs, an eNB can schedule MTC devices to use these PRBs to enhance the throughput performance. Simulation results show that either in a homogeneous MTC device network or in a heterogeneous MTC device network, the proposed CACB-LB's average access delay of UEs/MTC devices and average throughput from UEs/MTC devices are better than CACB's. The proposed CACB-LB with TARRM's average throughput from UEs/MTC devices is also higher than CACB's. Therefore, the proposed CACB-LB with TARRM is feasible for M2M communications over LTE-A.