Multi-tier heterogeneous networks have become an essential constituent for next generation cellular networks. Meanwhile, energy efficiency (EE) has been considered a critical design criterion along with the traditional spectral efficiency (SE) metric. In this context, we study power and spectrum allocation for the recently proposed two-tier network architecture known as phantom cellular networks. The optimization framework includes both EE and SE. First, we consider sparsely deployed cells experiencing negligible interference and assume perfect channel state information (CSI). For this setting, we propose an algorithm that finds the SE and EE resource allocation strategies. Then, we compare the performance of both design strategies versus number of users, and phantom cells share of the total available resource units (RUs). We aim to investigate the effect of some system parameters to achieve improved SE performance at a non-significant loss in EE performance, or vice versa. It is found that increasing phantom cells share of RUs decreases the SE performance loss due to EE optimization when compared with the optimized SE performance. Second, we consider the densely deployed phantom cellular networks and model the EE optimization problem having into consideration the inevitable interference and imperfect channel estimation. To this end, we propose three resource allocation strategies aiming at optimizing the EE performance metric of this network. Furthermore, we investigate the effect of changing some of the system parameters on the performance of the proposed strategies, such as phantom cells share of RUs, number of deployed phantom cells within a macro cell coverage, number of pilots and the maximum power available for transmission by the phantom cells BSs. It is found that increasing the number of pilots deteriorates the EE performance of the whole setup, while increasing maximum power available for phantom cells transmissions reduces the EE of the whole setup in a less severe way than increasing the number of pilots. It is found also that increasing phantom cells share increases the EE metric in the dense deployment case. Thus, it is always useful to allocate most of the network RUs to the phantom cells tier.