Combining thermodynamic measurements with theoretical calculations we demonstrate that the iridates A 2IrO 3 (A=Na, Li) are magnetically ordered Mott insulators where the magnetism of the effective spin-orbital S=1/2 moments can be captured by a Heisenberg-Kitaev (HK) model with interactions beyond nearest-neighbor exchange. Experimentally, we observe an increase of the Curie-Weiss temperature from θ-125K for Na 2IrO 3 to θ-33K for Li 2IrO 3, while the ordering temperature remains roughly the same T N 15K. Using functional renormalization group calculations we show that this evolution of θ and T N as well as the low temperature zigzag magnetic order can be captured within this extended HK model. We estimate that Na 2IrO 3 is deep in a magnetically ordered regime, while Li 2IrO 3 appears to be close to a spin-liquid regime. © 2012 American Physical Society.