Random spatial models are attractive for modeling heterogeneous cellular networks (HCNs) due to their realism, tractability, and scalability. A major limitation of such models to date in the context of HCNs is the neglect of network traffic and load: all base stations (BSs) have typically been assumed to always be transmitting. Small cells in particular will have a lighter load than macrocells, and so their contribution to the network interference may be significantly overstated in a fully loaded model. This paper incorporates a flexible notion of BS load by introducing a new idea of conditionally thinning the interference field. For a K-tier HCN where BSs across tiers differ in terms of transmit power, supported data rate, deployment density, and now load, we derive the coverage probability for a typical mobile, which connects to the strongest BS signal. Conditioned on this connection, the interfering BSs of the i^{th} tier are assumed to transmit independently with probability p-i, which models the load. Assuming-reasonably-that smaller cells are more lightly loaded than macrocells, the analysis shows that adding such access points to the network always increases the coverage probability. We also observe that fully loaded models are quite pessimistic in terms of coverage. © 2002-2012 IEEE.