Small cell networks are widely considered as an efficient low-cost solution to enhance the coverage and capacity of cellular layers on top of being environmentally friendly due to their low energy consumption. However, due to their aggressive spectrum reuse, it is important to properly control interference in such networks before deploying them on a large-scale basis. In this paper, we investigate the joint admission and power control problem in two-tier small cell networks. We aim to maximize the number of small cell users that can be admitted at their desired quality-of-service (QoS) without violating the macrocell users' QoS. However, it can be computationally challenging to perform adaptation at the fast fading time-scale. It also requires substantial signaling overhead due to feedback of channel state information. Therefore, we propose a joint admission and power control method where the QoS metric used is outage constraint so that the algorithm can adapt at a much slower log-normal shadowing time-scale. Even though this joint admission and power control problem is NP-hard, convex relaxation can be used to obtain high quality approximate solutions that demonstrate near optimal performance.